Question

Giải các phương trình:

a) \(\sqrt[3]{7+x}+\sqrt{1-x}=2\)

b) \(\sqrt{16x+17}=8x-23\)

c) \(3\sqrt{x^2+3x}=\left(x+5\right).\left(2-x\right)\)

Answer 1

b: \(\Leftrightarrow\left\{{}\begin{matrix}x>=\dfrac{23}{8}\\64x^2-368x+529-16x-17=0\end{matrix}\right.\)

\(\Leftrightarrow\left\{{}\begin{matrix}x>=\dfrac{23}{8}\\64x^2-384x+512=0\end{matrix}\right.\Leftrightarrow x=4\)

c: \(\Leftrightarrow3\sqrt{x^2+3x}=\left(2x-x^2+10-5x\right)\)

\(\Leftrightarrow3\sqrt{x^2+3x}=-\left(x^2+3x-10\right)\)

Đặt \(\sqrt{x^2+3x}=a\)

Ta có: \(3a=-\left(a^2-10\right)=-a^2+10\)

\(\Leftrightarrow a^2+3a-10=0\)

=>(a+5)(a-2)=0

=>a=2

=>x²+3x=4

=>(x+4)(x-1)=0

=>x=1 hoặc x=-4