Question

si x2+x-1=0 entonces x3+2x2+2015 es igual a:

Answer 1

$x^2+x-1=0 \\ x= \frac{-1\pm \sqrt{1^2-(4*1*-1)} }{2*1} \\ x= \frac{-1\pm \sqrt{1+4} }{2}= \frac{-1\pm \sqrt{5} }{2}\\ x_1= \frac{-1+ \sqrt{5} }{2} \\ x_2= \frac{-1- \sqrt{5} }{2} \\ \\ x^3+2x^2+2015 \\ \\ ( \frac{-1+ \sqrt{5} }{2})^3+2(\frac{-1+ \sqrt{5} }{2})^2+2015 \\ =(\frac{-1+3*1* \sqrt{5}+3*-1*5+5 \sqrt{5}}{8})+2( \frac{1+2*-1* \sqrt{5}+5 }{4})+2015 \\ = \frac{-1+3\sqrt{5}-15+5\sqrt{5}}{8}+ \frac{2-4\sqrt{5}+10}{4}+2015\\ =\frac{-16+8\sqrt{5}}{8}+ \frac{12-4\sqrt{5}}{4}+2015$
$=-2+\sqrt{5}+3-\sqrt{5}+2015\\ =1+2015 \\ =2016$

$x^3+2x^2+2015 \\ =( \frac{-1-\sqrt{5}}{2} )^3 +2( \frac{-1-\sqrt{5}}{2})^2+2015 \\ = \frac{-16-8\sqrt{5}}{8}+2( \frac{6+2\sqrt{5}}{4}) +2015 \\ -2-\sqrt{5}+ \frac{12+4\sqrt{5}}{4} +2015\\=-2-\sqrt{5}+3+\sqrt{5}+2015 \\=-2+3+2015 \\ =1+2015 \\ =2016$

Respuesta: x³+2x²+2015=2016

Answer 2

Respuesta:

Dale la corona se lo merece :)

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