Question

giải pt

a) \(x+4\sqrt{7-x}=4\sqrt{x-1}+\sqrt{-x^2+8x-7}+1\)

b) \(x^4-16x^3+46x^2+144x+81=0\)

c) \(x-\sqrt{x-8}-3\sqrt{x}+1=0\)

d) \(x^2+\sqrt{x+5}=5\)

e) \(x+\sqrt{5+\sqrt{x-1}}=6\)

Answer 1

b,

+ Với \(x=0\) \(\Rightarrow PTVN\)

+ Với \(x\ne0\), chia cả 2 vế cho \(x^2\) :

\(PT\Leftrightarrow x^2-16x+46+\frac{144}{x}+\frac{81}{x^2}=0\)

\(\Leftrightarrow\left(x^2+\frac{81}{x^2}\right)-16\left(x-\frac{9}{x}\right)+46=0\)

Đặt \(x-\frac{9}{x}=t\Rightarrow t^2=x^2+\frac{81}{x^2}-18\)

\(\Leftrightarrow t^2+18-16t+46=0\)

\(\Leftrightarrow t^2-16t+64=0\Rightarrow t=8\)

\(\Leftrightarrow x-\frac{9}{x}=8\Leftrightarrow x^2-8x-9=0\) \(\Rightarrow\left[{}\begin{matrix}x=-1\\x=9\end{matrix}\right.\) (t/m)