Question

giải phương trình

\(a,4\sqrt{x}-2\sqrt{9x}+\sqrt{16x}=5\)

\(b,\sqrt{4x+20}-3\sqrt{5+x}+\dfrac{4}{3}\sqrt{9x+45}=6\)

Help me!!!

Answer 1

Lời giải:

a) ĐK: \(x\geq 0\)

\(4\sqrt{x}-2\sqrt{9x}+\sqrt{16x}=5\)

\(\Leftrightarrow 4\sqrt{x}-2\sqrt{9}.\sqrt{x}+\sqrt{16}.\sqrt{x}=5\)

\(\Leftrightarrow 4\sqrt{x}-6\sqrt{x}+4\sqrt{x}=5\)

\(\Leftrightarrow 2\sqrt{x}=5\Rightarrow \sqrt{x}=\frac{5}{2}\Rightarrow x=\frac{25}{4}\) (thỏa man)

b) ĐK: \(x\geq -5\)

PT \(\Leftrightarrow \sqrt{4}.\sqrt{x+5}-3\sqrt{x+5}+\frac{4}{3}\sqrt{9}.\sqrt{x+5}=6\)

\(\Leftrightarrow 2\sqrt{x+5}-3\sqrt{x+5}+4\sqrt{x+5}=6\)

\(\Leftrightarrow 3\sqrt{x+5}=6\Rightarrow \sqrt{x+5}=2\)

\(\Rightarrow x+5=2^2=4\Rightarrow x=-1\) (thỏa mãn)