Question

Giải các phương trình sau:

\(a,\sqrt{1-4x+4x^2}=5\)

\(b,\sqrt{4-5x}=12\)

\(c,\sqrt{x-1}+\sqrt{4x-4}-\sqrt{25x-25}+2=0\)

\(d,\dfrac{1}{2}\sqrt{x-1}-\dfrac{3}{2}\sqrt{9x-9}+24\sqrt{\dfrac{x-1}{64}}=-17\)

Answer 1

a,

\(\sqrt{1-4x+4x^2}=5\\ \sqrt{\left(2x-1\right)^2}=5\\ \left[{}\begin{matrix}2x-1=5\\2x-1=-5\end{matrix}\right.\\ \left[{}\begin{matrix}x=3\\x=-2\end{matrix}\right.\)

Answer 2

b,

\(\sqrt{4-5x}=12\\ 4-5x=144\\ x=-28\)

Answer 3

c,

\(\sqrt{x-1}+\sqrt{4\left(x-1\right)}-\sqrt{25\left(x-1\right)}+2=0\\ \sqrt{x-1}+2\sqrt{x-1}-5\sqrt{x-1}+2=0\\ 2\left(1-\sqrt{x-1}\right)=0\\ 1-\sqrt{x-1}=0\\ \sqrt{x-1}=1\\ x-1=1\\ x=2\)