Question

1)Rezolavati In R ecuatia :(2x-3)(2x+4) -(2x+4) ^2 = 3(x-2) - 2x^2
2)Solutiile intregi ale ecuatiei 2x+4 mai mic sau egal decat -8 sunt

Answer 1

$(2x-3)(2x+4)-(2x+4)^{2}=3(x-2)-2x^{2}$
$4x^{2}+8x-6x-12-(4x^{2}+16x+16)=3x-6-2x^{2}$
$4x^{2}+8x-6x-12-4x^{2}-16x-16=3x-6-2x^{2}$
$-14x-28=3x-6-2x^{2}$
$-14x-28-3x+6+2x^{2}=0$
$-17x-22+2x^{2}=0$
$2x^{2}-17x-22=0$
$x=\dfrac{-(-17)\pm\sqrt{(-17)^{2}-4\cdot2\cdot(-22)}}{2\cdot2}$
$\dfrac{17\pm\sqrt{287+176}}{4}$
$x_{1}=\dfrac{17+\sqrt{465}}{4}$
$x_{2}=\dfrac{17-\sqrt{465}}{4}$

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$2x+4\leq-8$
$2x\leq-8-4$
$2x\leq-12$
$x\leq-6$