Question

Пример во вложении, спасибо заранее!

Answer 1

$25*25^{2x- x^{2} }+9*9^{2x- x^{2} }=34*15^{2x- x^{2} } | :9^{2x- x^{2} } \\ \\ 25* ((\frac{5}{3})^{2x- x^{2}})^{2 } +9=34*( \frac{5}{3}) ^{2x- x^{2} } \\ \\ y=( \frac{5}{3}) ^{2x- x^{2} } \\ \\ 25 y^{2}-34y+9=0 \\ \\ y_{1,2} = \frac{34б \sqrt{34^{2}-4*25*9} }{2*25} \\ \\ y_{1,2} = \frac{34б 16 }{50} \\ \\ y_{1}=1; y_{2} =\frac{9}{25} \\ \\ ( \frac{5}{3}) ^{2x- x^{2} }=1 \\ 2x- x^{2} =0 \\ x_{1}=0 ; x_{2}=2$

$\\ (\frac{5}{3}) ^{2x- x^{2} }= \frac{9}{25} \\ \\ 2x- x^{2} =-2 \\ x^{2} -2x-2=0 \\ x_{3,4} = \frac{2б \sqrt{4+8} }{2} =1б \sqrt{3}$
Ответ: х∈{1-√3;0;2;1+√3}