Question

phan tich ;can (x+10x+21)=3can(x+3) + 2can(x+7)-6

Answer 1

Sửa đè \(\sqrt{x^2+10x+21}=3\sqrt{x+3}+2\sqrt{x+7}-6\)

Đk:\(x\ge-3\)

\(pt\Leftrightarrow\sqrt{\left(x+3\right)\left(x+7\right)}=3\sqrt{x+3}+2\sqrt{x+7}-6\)

Đặt \(\hept{\begin{cases}\sqrt{x+3}=a\\\sqrt{x+7}=b\end{cases}\left(a,b>0\right)}\) thì 

\(\Leftrightarrow ab=3a+2b-6\)

\(\Leftrightarrow\left(a-2\right)\left(b-3\right)=0\Rightarrow\orbr{\begin{cases}a=2\\b=3\end{cases}}\)

\(\Rightarrow\orbr{\begin{cases}\sqrt{x+3}=2\\\sqrt{x+7}=3\end{cases}}\)\(\Rightarrow\orbr{\begin{cases}x=1\\x=2\end{cases}}\) (thỏa)

Answer 2

ban oi viet dau can kieu gi vay