Question

Найти x 80 баллов!!!!

Answer 1

$(0,2^{\sqrt{x+1}})^{\sqrt{x+6}} =\frac{1}{5} \\ (\frac{1}{5}^{\sqrt{x+1}})^{\sqrt{x+6}}=(\frac{1}{5})^1 \\ \sqrt{x+1}\cdot\sqrt{x+6}=1 \\ \sqrt{(x+1)(x+6)}=1 \\ (\sqrt{(x+1)(x+6)})^2=1^2 \\ (x+1)(x+6)=1 \\ x^2+7x+6=1 \\ x^2+7x+5=0 \\ D = b^2-4ac=7^2-4\cdot1\cdot5=49-20=29 \\ x_{1} = \frac{-b-\sqrt{D}}{2a}=\frac{-7-\sqrt{29}}{2\cdot1} \\ x_{2} = \frac{-b+\sqrt{D}}{2a}=\frac{-7+\sqrt{29}}{2\cdot1}$