Question

Решите уравнение : x^8=(2x+3)^4

Answer 1

${x}^{8} = (2x + 3)^{4} \\ x {}^{2} = |2x + 3| \\ 1)2x + 3 \geqslant 0 \\ x \geqslant - \frac{3}{2} \\ {x}^{2} - 2x - 3 = 0 \\ D/4=1+3=4\\x_{1} =1+2=3 \: and \: \: x_{2}=1-2= - 1 \\ 2)2x + 3 < 0 \\ x < - \frac{ 3}{2} \\ {x}^{2} + 2x + 3 = 0 \\ D/4 =1-3= - 2 \\x \notin\mathbb R$

Ответ: х=3;-1