Question

Aflati x1 si x2 daca:
7x^2-2x-14=0
x^2-2/7x-2=0
x1=? x1+x2=-2/7
=>
x2=? x1*x2=-2

Answer 1

$x_1+x_2=-\dfrac{-2}7=\dfrac{2}7\Rightarrow x_1=\dfrac{2}7-x_2\\\\x_1\cdot x_2=\dfrac{-14}7=-2\Rightarrow\left(\dfrac{2}7-x_2\right)\cdot x_2=-2\;\Big|\cdot 7,\\\\sau\;(2-7x_2)x_2=-14\Rightarrow 7x_2^2-2x_2-14=0$

Am ajuns deci la relaţia din enunţ, care se rezolvă cu clasica formulă:

$x_{1,2}=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}.$

Green eyes.