Question

3. Rezolvați ecuația (x + 3)2 + (x + 5)(x – 5) = 4(x – 3).

Answer 1

Răspuns:

Explicație:

$\bf (x + 3)^2 + (x+5)\cdot(x-5) = 4(x-3)$

$\bf (x + 3)^2 + (x^2-5^2)= 4(x-3)$

$\bf x^2+6x+3^2 + x^2-25= 4(x-3)$

$\bf 2x^2+6x+9 -25= 4(x-3)$

$\bf 2x^2+6x-16= 4(x-3)~~~~\bigg|:2$

$\bf x^2+3x-8= 2(x-3)$

$\bf x^2+3x-8= 2x-6$

$\bf x^2+3x-8- 2x+6=0$

$\bf x^2+x-2=0$

$\bf x^2+2x-x-2=0$

$\bf x\cdot(x+2)-(x+2)=0$

$\bf (x+2)\cdot(x-1)=0\implies$

$\bf x+2=0\implies \red{\underline{x_{1}=-2}}$

$\bf x-1=0\implies \red{\underline{x_{2}=1}}$

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