Question

Giải phương trình:

a) cân ( x^2 - 25 ) = 2 × cân ( x - 5 )

b) cân x + 1/ cân x = 2

c) cân ( x - 5 ) + 1/3 cân ( 9x - 45 ) = 1/5 cân ( 25x - 125 ) + 6

Answer 1

a) Đk \(x\ge\pm5\)\(\sqrt{x^2-25}=2.\sqrt{x-5}\Leftrightarrow x^2-25=4\left(x-5\right)\Leftrightarrow x+5=4\Leftrightarrow x=-1\)

Answer 2

b) \(\sqrt{x}+\frac{1}{\sqrt{x}}=2\Leftrightarrow x+1-2\sqrt{x}=0\)\(\Leftrightarrow\left(\sqrt{x}-1\right)^2=0\Leftrightarrow x=1\)

Answer 3

c) \(\sqrt{x-5}+\frac{1}{3}\sqrt{9x-45}=\frac{1}{5}\sqrt{25x-125}+6\)

\(\Leftrightarrow\sqrt{x-5}+\frac{1}{3}\sqrt{9\left(x-5\right)}=\frac{1}{5}\sqrt{25\left(x-5\right)}+6\)

\(\Leftrightarrow\left(\sqrt{x}-5\right)\left(1+1-1-6\right)=0\Leftrightarrow-5\left(\sqrt{x}-5\right)=0\Rightarrow\sqrt{x}-5=0\Leftrightarrow x=25\)