Question

giúp mình vs !! Gấp .....................................

Answer 1

a.

ĐKXĐ: \(x\ge-1\)

\(\Leftrightarrow\left(x+1-4\sqrt{x+1}+4\right)+\left(2x+3-6\sqrt{2x+3}+9\right)=0\)

\(\Leftrightarrow\left(\sqrt{x+1}-2\right)^2+\left(\sqrt{2x+3}-3\right)^2=0\)

\(\Leftrightarrow\left\{{}\begin{matrix}\sqrt{x+1}-2=0\\\sqrt{2x+3}-3=0\end{matrix}\right.\)

\(\Leftrightarrow x=3\)

b.

Ta có:

\(VT=\sqrt{2-x}+\sqrt{7+x}\ge\sqrt{2-x+7+x}=3\)

\(VP=-\left(x-2\right)^2+3\le3\)

Đẳng thức xảy ra khi và chỉ khi:

\(\left\{{}\begin{matrix}\left(2-x\right)\left(7+x\right)=0\\x-2=0\end{matrix}\right.\) \(\Leftrightarrow x=2\)