Question

Giải pt \(x+4\sqrt{x+3}+2\sqrt{3-2x}=11\)

Answer 1

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

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

=> x-1+\(\dfrac{4.\left(x-1\right)}{\sqrt{x+3}+2}+\dfrac{4.\left(1-x\right)}{\sqrt{3-2x}+1}=0\)

=> (x-1).\(\left(\dfrac{4}{\sqrt{x+3}+2}+\dfrac{4}{\sqrt{3-2x}+1}\right)=0\)

=> x=1 (do \(\dfrac{4}{\sqrt{x+3}+2}+\dfrac{4}{\sqrt{3-2x}+1}>0\)