Question

Решить 25∧х +2*а*5∧х +а∧2=0, -3 ∠ х ≤2

Answer 1

$25^x+2a\cdot 5^x+a^2=0\\5^{2x}+2a\cdot 5^x+a^2=0\\5^x=b,b>0\Rightarrow b^2+2ab+a^2=0\\(a+b)^2=0\Rightarrow a+b=0\\a=-b\Rightarrow a=-5^x\Rightarrow x=log_5(-a)$