Question

Решите уравнение....

Answer 1

$\displaystyle \sqrt[x]{5^{5 \sqrt{x}}}=5^{ \sqrt{x} -4}\\\\ODZ: X\ \textgreater \ 0 \\\\5^{ \frac{5 \sqrt{x}} {x}}=5^{ \sqrt{x} -4}\\\\ \frac{5 \sqrt{x} }{x}= \sqrt{x} -4\\\\ \frac{5}{ \sqrt{x} }= \sqrt{x} -4\\\\ \sqrt{x} =t\\\\5=t^2-4t\\\\t^2-4t-5=0\\\\D=16+20=36\\\\t_{1.2}= \frac{4\pm 6}{2}\\\\t_1= 5; t_2=-1$

$\displaystyle \sqrt{x} =5\\\\x=25$

$\displaystyle \sqrt{x} \neq -1$

Ответ х=25