Question

aflati valoarea lui x pentru care sunt egale expresiile (x-4)(x+6)si (x-6)^{2} -4

Answer 1

Răspuns:

Explicație pas cu pas:

$\frac{x-4}{x+6} =(x-6)^{2} -4\\\frac{x-4}{x+6}=(x-6-2)(x-6+2)\\\frac{x-4}{x+6}=(x-8)(x-4)\\\frac{x-4}{x+6}-(x-8)(x-4)=0\\(x-4)(\frac{1}{x+6} -x+8)=0\\x-4=0\\x=4\\\\\frac{1}{x+6} -x+8=0$

1-x(x+6)+8(x+6)=0

1-x²-6x+8x+48=0

-x²+2x+49=0

x²-2x-49=0

Δ=200

$x_{1}=\frac{2+10\sqrt{2} }{2} =1+5\sqrt{2} \\x_{2}=\frac{2-10\sqrt{2} }{2} =1-5\sqrt{2}$