Question

Sa se formeze ecuația de gradul || dacă se cunosc rădăcinile x1=3-radical din 5, x2=3+radical din 5

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Answer 1

 

$\displaystyle\bf\\Daca~se~cunosc~radacinile~x_1~si~x_2, ecuatia~de~gradul~2\\se~formeaza~cu~formeaza~(se~compune)~cu~formula:\\\\(x-x1)(x-x_2)=0\\\\Rezolvare:\\\\x_1=3-\sqrt{5}\\\\x_2=3+\sqrt{5}$

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$\displaystyle\bf\\Ecuatia~va~fi:\\\\~\Big[x-(3-\sqrt{5})\Big]\Big[x-(3+\sqrt{5})\Big]=0\\\\Aducem~ecuatia~la~o~forma~mai~simpla.\\\\x^2-x(3-\sqrt{5})-x(3+\sqrt{5})+(3-\sqrt{5})(3+\sqrt{5})=0\\\\x^2-3x+x\sqrt{5}-3x-x\sqrt{5}+3^2-\Big(\sqrt{5}\Big)^2=0\\\\x^2-3x-3x+x\sqrt{5}-x\sqrt{5}+9-5=0\\\\x^2-6x+0+4=0\\\\\boxed{\bf x^2-6x+4=0}$