Question

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

Answer 1

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

ответ : x=8