Question

2x$\sqrt{5x+24}$=$x^{2}$+5x+24

Answer 1

$2x \sqrt{5x+24} =x^2+5x+24 \\ \\ x^2-2x\sqrt{5x+24}+(\sqrt{5x+24})^2=0 \\ \\ (x-\sqrt{5x+24})^2=0 \\ \\ x=\sqrt{5x+24} \\ \\ x^2=5x+24 \\ \\ x^2-5x-24=0 \\ \\ D=25+4*24=121=11^2 \\ \\ x_{1} =(5+11)/2=8 \\ \\ 2*8 \sqrt{5*8+24} =8^2+5*8+24 \\ 16*8=64+40+24 \\ 128=128 \\ \\ x_{2} =(5-11)/2=-3 \\ \\ 2*(-3) \sqrt{5*(-3)+24} \neq 9-15+24 \\ \\ -18 \neq 18$
посторонний корень

ответ : x=8