{"id":217,"date":"2025-11-16T09:06:07","date_gmt":"2025-11-16T09:06:07","guid":{"rendered":"https:\/\/maths4u.gr\/wordpress\/?page_id=217"},"modified":"2025-11-16T09:06:07","modified_gmt":"2025-11-16T09:06:07","slug":"trionymo","status":"publish","type":"page","link":"https:\/\/maths4u.gr\/index.php\/trionymo\/","title":{"rendered":"\u03a4\u03c1\u03b9\u03ce\u03bd\u03c5\u03bc\u03bf \u0392! \u0392\u03b1\u03b8\u03bc\u03bf\u03cd"},"content":{"rendered":"<h1><a id=\"par1\"><\/a>\u0395\u03c0\u03b9\u03bb\u03b5\u03b3\u03bc\u03ad\u03bd\u03b5\u03c2 \u0391\u03c3\u03ba\u03ae\u03c3\u03b5\u03b9\u03c2 \u0395\u03be\u03b9\u03c3\u03ce\u03c3\u03b5\u03c9\u03bd \u0392&#8217; \u0392\u03b1\u03b8\u03bc\u03bf\u03cd<\/h1>\n<p>\u039d\u03b1 \u03ad\u03c7\u03b5\u03c4\u03b5 \u03c3\u03c4\u03bf \u03bc\u03c5\u03b1\u03bb\u03cc \u03c3\u03b1\u03c2 \u03cc\u03c4\u03b9:<br \/>\n(\u03b1) \u039f\u03b9 \u03c1\u03af\u03b6\u03b5\u03c2 \u03bc\u03b9\u03b1\u03c2 \u03b4\u03b5\u03c5\u03c4\u03b5\u03c1\u03bf\u03b2\u03ac\u03b8\u03bc\u03b9\u03b1\u03c2 \u03b5\u03be\u03af\u03c3\u03c9\u03c3\u03b7\u03c2, \u03ad\u03c3\u03c4\u03c9 \u03c4\u03b7\u03c2 \\(ax^2+bx+c=0\\) \u03b4\u03af\u03bd\u03bf\u03bd\u03c4\u03b1\u03b9 \u03b1\u03c0\u03cc \u03c4\u03bf\u03bd \u03c4\u03cd\u03c0\u03bf \\(x_{1,2}=\\dfrac{-b\\pm \\sqrt{b^2-4ac}}{2a}.\\)<br \/>\n(\u03b2) \u0399\u03c3\u03c7\u03cd\u03bf\u03c5\u03bd \u03bf\u03b9 \u03b5\u03be\u03ae\u03c2 \u03c3\u03c7\u03ad\u03c3\u03b5\u03b9\u03c2 \u03bc\u03b5\u03c4\u03b1\u03be\u03cd \u03c4\u03c9\u03bd \u03c1\u03b9\u03b6\u03ce\u03bd: \\(x_1+x_2=-\\dfrac{b}{a}\\) \u03ba\u03b1\u03b9 \\(x_1\\cdot x_2=\\dfrac{c}{a}.\\)<\/p>\n<div>\n<p>\\(\\textbf{\u0386\u03c3\u03ba\u03b7\u03c3\u03b7 1}\\). \u039d\u03b1 \u03bb\u03cd\u03c3\u03b5\u03c4\u03b5 \u03c4\u03b9\u03c2 \u03b5\u03be\u03b9\u03c3\u03ce\u03c3\u03b5\u03b9\u03c2: (\u03b1).\\(\\; x^2-2x-1=0,\\quad\\) (\u03b2). \\(2x+\\dfrac{21}{x+3}=9,\\quad\\) (\u03b3). \\(\\dfrac{3}{x}+\\dfrac{5}{x-2}=0.\\quad\\)<\/p>\n<p>\\(\\textbf{\u0386\u03c3\u03ba\u03b7\u03c3\u03b7 2}\\). \u039d\u03b1 \u03c0\u03c1\u03bf\u03c3\u03b4\u03b9\u03bf\u03c1\u03af\u03c3\u03b5\u03c4\u03b5 \u03c4\u03b9\u03c2 \u03c4\u03b9\u03bc\u03ad\u03c2 \u03c4\u03bf\u03c5 \\(\\kappa\\) \u03ce\u03c3\u03c4\u03b5 \u03bf\u03b9 \u03c1\u03af\u03b6\u03b5\u03c2 \u03ba\u03ac\u03b8\u03b5 \u03bc\u03b9\u03b1\u03c2 \u03b1\u03c0\u03cc \u03c4\u03b9\u03c2 \u03c0\u03b1\u03c1\u03b1\u03ba\u03ac\u03c4\u03c9 \u03b5\u03be\u03b9\u03c3\u03ce\u03c3\u03b5\u03b9\u03c2 \u03bd\u03b1 \u03b5\u03af\u03bd\u03b1\u03b9 \u03af\u03c3\u03b5\u03c2:<br \/>\n\\(\\quad 9x^2+12x+\\kappa=0,\\quad 9x^2+2\\kappa x+16=0, \\quad \\kappa x^2+2\\kappa x+9=x^2-2x \\)<\/p>\n<p>\u03a5\u03c0\u03cc\u03b4\u03b5\u03b9\u03be\u03b7: \u03a0\u03c1\u03ad\u03c0\u03b5\u03b9 \u03b7 \u03b4\u03b9\u03b1\u03ba\u03c1\u03af\u03bd\u03bf\u03c5\u03c3\u03b1 \u03ba\u03ac\u03b8\u03b5 \u03bc\u03b9\u03b1\u03c2 \u03bd\u03b1 \u03b5\u03af\u03bd\u03b1\u03b9 \u03af\u03c3\u03b7 \u03bc\u03b5 \u03bc\u03b7\u03b4\u03ad\u03bd.<\/p>\n<p>\\(\\textbf{\u0386\u03c3\u03ba\u03b7\u03c3\u03b7 3}\\). \u039d\u03b1 \u03b2\u03c1\u03b5\u03af\u03c4\u03b5 \u03c4\u03b9\u03c2 \u03c0\u03c1\u03b1\u03b3\u03bc\u03b1\u03c4\u03b9\u03ba\u03ad\u03c2 \u03c1\u03af\u03b6\u03b5\u03c2 \u03c4\u03b7\u03c2 \u03b5\u03be\u03af\u03c3\u03c9\u03c3\u03b7\u03c2:\\(\\quad x^2-2x+\\vert5-3x\\vert=0\\).<\/p>\n<p>\\(\\textbf{\u0386\u03c3\u03ba\u03b7\u03c3\u03b7 4}\\). \u039d\u03b1 \u03bb\u03c5\u03b8\u03bf\u03cd\u03bd \u03bf\u03b9 \u03b5\u03be\u03b9\u03c3\u03ce\u03c3\u03b5\u03b9\u03c2: \\(\\quad \\sqrt{7x+14}=x+2,\\quad \\sqrt{5x-4}=2+\\sqrt{2x}.\\)<\/p>\n<p>\\(\\textbf{\u0386\u03c3\u03ba\u03b7\u03c3\u03b7 5}\\). \u0391\u03bd \u03bf\u03b9 \u03c1\u03af\u03b6\u03b5\u03c2 \u03c4\u03b7\u03c2 \\(ax^2+bx+c=0\\) \u03b5\u03af\u03bd\u03b1\u03b9 \u03bf\u03b9 \\(x_1,\\, x_2\\), \u03bd\u03b1 \u03b2\u03c1\u03b5\u03b8\u03bf\u03cd\u03bd \u03c3\u03c5\u03bd\u03b1\u03c1\u03c4\u03ae\u03c3\u03b5\u03b9 \u03c4\u03c9\u03bd \\(x_1,\\, x_2\\) \u03bf\u03b9 \u03c1\u03af\u03b6\u03b5\u03c2 \u03c4\u03b7\u03c2<br \/>\n\\(x+2+\\dfrac{1}{x}=\\dfrac{b^2}{a\\cdot c}\\)<\/p>\n<p>\\(\\textbf{\u0386\u03c3\u03ba\u03b7\u03c3\u03b7 6}\\). \u039d\u03b1 \u03bf\u03c1\u03af\u03c3\u03b5\u03c4\u03b5 \u03c4\u03b1 \\(\\lambda, \\mu\\) \u03cc\u03c4\u03b1\u03bd \u03b3\u03bd\u03c9\u03c1\u03af\u03b6\u03bf\u03c5\u03bc\u03b5 \u03cc\u03c4\u03b9 \u03bf\u03b9 \u03c1\u03af\u03b6\u03b5\u03c2 \u03c4\u03b7\u03c2 \\(x^2+\\lambda x+\\mu=0\\), \u03cc\u03c4\u03b1\u03bd \u03b1\u03c5\u03be\u03ac\u03bd\u03bf\u03bd\u03c4\u03b1\u03b9 \u03ba\u03b1\u03c4\u03ac 1, \u03b3\u03af\u03bd\u03bf\u03bd\u03c4\u03b1\u03b9 \u03c1\u03af\u03b6\u03b5\u03c2 \u03c4\u03b7\u03c2<br \/>\n\\(x^2-\\lambda^2 x+\\lambda \\mu=0.\\)<\/p>\n<p>\\(\\textbf{\u0386\u03c3\u03ba\u03b7\u03c3\u03b7 7}\\). \u039d\u03b1 \u03bf\u03c1\u03af\u03c3\u03b5\u03c4\u03b5 \u03c4\u03bf \\(\\lambda\\) \u03ce\u03c3\u03c4\u03b5 \u03b7 \u03bc\u03b9\u03b1 \u03c1\u03af\u03b6\u03b1 \u03c4\u03b7\u03c2 \u03b5\u03be\u03af\u03c3\u03c9\u03c3\u03b7\u03c2 \\(3x^2-20x+3\\lambda +1=0\\) \u03bd\u03b1 \u03b5\u03af\u03bd\u03b1\u03b9 \u03c4\u03c1\u03b9\u03c0\u03bb\u03ac\u03c3\u03b9\u03b1 \u03c4\u03b7\u03c2 \u03ac\u03bb\u03bb\u03b7\u03c2.<\/p>\n<p>\\(\\textbf{\u0386\u03c3\u03ba\u03b7\u03c3\u03b7 8}\\). \u039d\u03b1 \u03b2\u03c1\u03b5\u03af\u03c4\u03b5 \u03c4\u03bf \u03c0\u03b5\u03b4\u03af\u03bf \u03bf\u03c1\u03b9\u03c3\u03bc\u03bf\u03cd \u03c4\u03b7\u03c2 \u03c3\u03c5\u03bd\u03ac\u03c1\u03c4\u03b7\u03c3\u03b7\u03c2 \\(f(x)=5\\sqrt{x^2-4x+3}-2\\sqrt{-x^2+6x+8}.\\)<\/p>\n<\/div>\n<h1><a id=\"par1\"><\/a>\u0395\u03c0\u03b9\u03bb\u03b5\u03b3\u03bc\u03ad\u03bd\u03b5\u03c2 \u0391\u03c3\u03ba\u03ae\u03c3\u03b5\u03b9\u03c2 \u0391\u03bd\u03b9\u03c3\u03ce\u03c3\u03b5\u03c9\u03bd \u0392&#8217; \u0392\u03b1\u03b8\u03bc\u03bf\u03cd<\/h1>\n<div>\n<p>\\(\\textbf{\u0386\u03c3\u03ba\u03b7\u03c3\u03b7 1}\\). \u039d\u03b1 \u03bb\u03c5\u03b8\u03bf\u03cd\u03bd \u03bf\u03b9 \u03b1\u03bd\u03b9\u03c3\u03cc\u03c4\u03b7\u03c4\u03b5\u03c2: (\u03b1).\\(\\; 3x^3-5x^2+2x&gt;0, \\quad\\) (\u03b2). \\(\\; \\dfrac{x^2-7x+12}{x^2-17x+60}&gt;0, \\quad\\) (\u03b3). \\(\\; 3+\\dfrac{1}{3-x}&gt;\\dfrac{3}{5x+1}.\\quad\\)<\/p>\n<p>\\(\\textbf{\u0386\u03c3\u03ba\u03b7\u03c3\u03b7 2}\\). \u0393\u03b9\u03b1 \u03c0\u03bf\u03b9\u03ad\u03c2 \u03c4\u03b9\u03bc\u03ad\u03c2 \u03c4\u03bf\u03c5 \\(x\\) \u03c3\u03c5\u03bd\u03b1\u03bb\u03b7\u03b8\u03b5\u03cd\u03bf\u03c5\u03bd \u03bf\u03b9 \u03b1\u03bd\u03b9\u03c3\u03cc\u03c4\u03b7\u03c4\u03b5\u03c2: \\(\\dfrac{3x-1}{x+2}&gt;0 \\quad\\) \u03ba\u03b1\u03b9 \\(\\quad \\dfrac{x^2+3x-4}{x(x+3)}&lt;0 \\quad\\)<\/p>\n<p>\\(\\textbf{\u0386\u03c3\u03ba\u03b7\u03c3\u03b7 3}\\). \u0393\u03b9\u03b1 \u03c0\u03bf\u03b9\u03ad\u03c2 \u03c4\u03b9\u03bc\u03ad\u03c2 \u03c4\u03bf\u03c5 \\(x\\) \u03c4\u03bf \u03c4\u03c1\u03b9\u03ce\u03bd\u03c5\u03bc\u03bf \\(\\quad x^2-14x+50 \\quad\\) \u03c0\u03b1\u03af\u03c1\u03bd\u03b5\u03b9 \u03c4\u03b9\u03bc\u03ad\u03c2 \u03bc\u03b5\u03b3\u03b1\u03bb\u03cd\u03c4\u03b5\u03c1\u03b5\u03c2 \u03c4\u03bf\u03c5 \\(5\\) \u03ba\u03b1\u03b9 \u03bc\u03b9\u03ba\u03c1\u03cc\u03c4\u03b5\u03c1\u03b5\u03c2 \u03c4\u03bf\u03c5 \\(26\\).<\/p>\n<p>\\(\\textbf{\u0386\u03c3\u03ba\u03b7\u03c3\u03b7 4}\\). \u0391\u03bd \\(x_1\\) \u03ba\u03b1\u03b9 \\(x_2\\) \u03b5\u03af\u03bd\u03b1\u03b9 \u03bf\u03b9 \u03c1\u03af\u03b6\u03b5\u03c2 \u03c4\u03bf\u03c5 \u03c4\u03c1\u03b9\u03c9\u03bd\u03cd\u03bc\u03bf\u03c5 \\(f(x)=(\\lambda-1)x^2-(\\lambda+1)x+\\lambda-2\\) \u03bd\u03b1 \u03b2\u03c1\u03b5\u03af\u03c4\u03b5 \u03b3\u03b9\u03b1 \u03c0\u03bf\u03b9\u03ad\u03c2 \u03c4\u03b9\u03bc\u03ad\u03c2 \u03c4\u03bf\u03c5 \\(\\lambda\\) \u03b7 \u03c0\u03b1\u03c1\u03ac\u03c3\u03c4\u03b1\u03c3\u03b7 \\(x_1^2-x_1x_2+x_2^2 \\quad\\) \u03b5\u03af\u03bd\u03b1\u03b9 \u03b8\u03b5\u03c4\u03b9\u03ba\u03ae \u03ba\u03b1\u03b9 \u03bc\u03b9\u03ba\u03c1\u03cc\u03c4\u03b5\u03c1\u03b7 \u03c4\u03bf\u03c5 \\(10\\).<\/p>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>\u0395\u03c0\u03b9\u03bb\u03b5\u03b3\u03bc\u03ad\u03bd\u03b5\u03c2 \u0391\u03c3\u03ba\u03ae\u03c3\u03b5\u03b9\u03c2 \u0395\u03be\u03b9\u03c3\u03ce\u03c3\u03b5\u03c9\u03bd \u0392&#8217; \u0392\u03b1\u03b8\u03bc\u03bf\u03cd \u039d\u03b1 \u03ad\u03c7\u03b5\u03c4\u03b5 \u03c3\u03c4\u03bf \u03bc\u03c5\u03b1\u03bb\u03cc \u03c3\u03b1\u03c2 \u03cc\u03c4\u03b9: (\u03b1) \u039f\u03b9 \u03c1\u03af\u03b6\u03b5\u03c2 \u03bc\u03b9\u03b1\u03c2 \u03b4\u03b5\u03c5\u03c4\u03b5\u03c1\u03bf\u03b2\u03ac\u03b8\u03bc\u03b9\u03b1\u03c2 \u03b5\u03be\u03af\u03c3\u03c9\u03c3\u03b7\u03c2, \u03ad\u03c3\u03c4\u03c9 \u03c4\u03b7\u03c2 \\(ax^2+bx+c=0\\) \u03b4\u03af\u03bd\u03bf\u03bd\u03c4\u03b1\u03b9 \u03b1\u03c0\u03cc \u03c4\u03bf\u03bd \u03c4\u03cd\u03c0\u03bf \\(x_{1,2}=\\dfrac{-b\\pm \\sqrt{b^2-4ac}}{2a}.\\) (\u03b2) \u0399\u03c3\u03c7\u03cd\u03bf\u03c5\u03bd \u03bf\u03b9 \u03b5\u03be\u03ae\u03c2 \u03c3\u03c7\u03ad\u03c3\u03b5\u03b9\u03c2 \u03bc\u03b5\u03c4\u03b1\u03be\u03cd \u03c4\u03c9\u03bd \u03c1\u03b9\u03b6\u03ce\u03bd: \\(x_1+x_2=-\\dfrac{b}{a}\\) \u03ba\u03b1\u03b9 \\(x_1\\cdot x_2=\\dfrac{c}{a}.\\) \\(\\textbf{\u0386\u03c3\u03ba\u03b7\u03c3\u03b7 1}\\). \u039d\u03b1 \u03bb\u03cd\u03c3\u03b5\u03c4\u03b5 \u03c4\u03b9\u03c2 \u03b5\u03be\u03b9\u03c3\u03ce\u03c3\u03b5\u03b9\u03c2: (\u03b1).\\(\\; x^2-2x-1=0,\\quad\\) (\u03b2). \\(2x+\\dfrac{21}{x+3}=9,\\quad\\) (\u03b3). \\(\\dfrac{3}{x}+\\dfrac{5}{x-2}=0.\\quad\\) \\(\\textbf{\u0386\u03c3\u03ba\u03b7\u03c3\u03b7 2}\\). \u039d\u03b1 \u03c0\u03c1\u03bf\u03c3\u03b4\u03b9\u03bf\u03c1\u03af\u03c3\u03b5\u03c4\u03b5 \u03c4\u03b9\u03c2 &hellip; <a href=\"https:\/\/maths4u.gr\/index.php\/trionymo\/\" class=\"more-link\">\u0394\u03b9\u03b1\u03b2\u03ac\u03c3\u03c4\u03b5 \u03c0\u03b5\u03c1\u03b9\u03c3\u03c3\u03cc\u03c4\u03b5\u03c1\u03b1<span class=\"screen-reader-text\"> &#8220;\u03a4\u03c1\u03b9\u03ce\u03bd\u03c5\u03bc\u03bf \u0392! \u0392\u03b1\u03b8\u03bc\u03bf\u03cd&#8221;<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":["post-217","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/maths4u.gr\/index.php\/wp-json\/wp\/v2\/pages\/217","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/maths4u.gr\/index.php\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/maths4u.gr\/index.php\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/maths4u.gr\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/maths4u.gr\/index.php\/wp-json\/wp\/v2\/comments?post=217"}],"version-history":[{"count":0,"href":"https:\/\/maths4u.gr\/index.php\/wp-json\/wp\/v2\/pages\/217\/revisions"}],"wp:attachment":[{"href":"https:\/\/maths4u.gr\/index.php\/wp-json\/wp\/v2\/media?parent=217"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}