Question

Как решить это уравнение ?

Answer 1

Ответ:

x = -4+2√5; -4-2√5; -6; -2

Обьяснение:

это разность квадратов

a^2-b^2 = (a-b)*(a+b)

a = x^2+8x+4

b = 1

(x^2+8x+4)^2 - 1^2 = 63

(x^2+8x+4)^2 = 64

получаем систему:

1) x^2+8x+4 = 8 => x = -4+2√5; -4-2√5

2) x^2+8x+4 = -8 => x = -6; -2

Answer 2

$\displaystyle\bf\\(x^{2} +8x+3)(x^{2} +8x+5)=63\\\\x^{2} +8x+3=m \ \ \ \Rightarrow \ \ \ x^{2} +8x+5=m+2\\\\m\cdot (m+2)-63=0\\\\m^{2} +2m-63=0\\\\D=2^{2} -4\cdot(-63)=4+252=256=16^{2} \\\\\\m_{1} =\frac{-2-16}{2} =-9\\\\\\m_{2} =\frac{-2+16}{2} =7\\\\\\1)\\\\x^{2} +8x+3=-9\\\\x^{2} +8x+12=0\\\\Teorema \ Vieta:\\x_{1} =-2 \ \ ; \ \ x_{2} =-6\\\\2)\\\\x^{2} +8x+3=7\\\\x^{2} +8x-4=0\\\\D=8^{2} -4\cdot(-4)=64+16=80=(4\sqrt{5} )^{2}$

$\displaystyle\bf\\x_{3} =\frac{-8-4\sqrt{5} }{2} =-4-2\sqrt{5} \\\\\\x_{4} =\frac{-8+4\sqrt{5} }{2} =2\sqrt{5} -4\\\\\\Otvet \ : \ -2 \ ; \ -6 \ ; \ -4-2\sqrt{5} \ ; \ 2\sqrt{5} -4$