Question

Giải phương trình:

a) \(\sqrt{2059-x}+\sqrt{2035-x}+\sqrt{2154-x}=24\)

b) \(x+4\sqrt{x+3}+2\sqrt{3-2x}=11\)

Answer 1

b) cách khác:

\(pt\Leftrightarrow11-x-4\sqrt{x+3}-2\sqrt{3-2x}=0\)

\(\Leftrightarrow3-2x-2\sqrt{3-2x}+1+x+3-4\sqrt{x+3}+4=0\)

\(\Leftrightarrow\left(\sqrt{3-2x}-1\right)^2+\left(\sqrt{x+3}-2\right)^2=0\)

\(\Leftrightarrow\sqrt{3-2x}-1=\sqrt{x+3}-2=0\)

\(\Leftrightarrow x=1\)

Answer 2

b liên hợp hoặc cosi, đặt ẩn cx đc

Answer 3

b)\(Pt\Leftrightarrow x-1+4\sqrt{x+3}-8+2\sqrt{3-2x}-2=0\)

\(\Leftrightarrow\left(x-1\right)+4\cdot\frac{x-1}{\sqrt{x+3}+2}+2\cdot\frac{2\left(1-x\right)}{\sqrt{3-2x}+1=0}\)

\(\Leftrightarrow\left(x-1\right)\left(1+\frac{4}{\sqrt{x+3}+2}-\frac{4}{\sqrt{3-2x}+1}\right)=0\)

\(\Leftrightarrow x=1\)