Question

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

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

(x-1)(x+2)+4(x-1)\(\sqrt{\frac{x+2}{x-1}}\)=12

Answer 1

a)\(\sqrt{x+2\sqrt{x-1}}+\sqrt{x-2\sqrt{x-1}}=2\) điều kiện x lớn hơn hoặc bằng 0

<=> \(\sqrt{\left(\sqrt{x-1}+1\right)^2}+\sqrt{\left(\sqrt{x-1}-1\right)^2}=2\)

<=> \(\sqrt{x-1}+1+\sqrt{x-1}-1=2\)

<=> \(2\sqrt{x-1}=2\)<=> \(\sqrt{x-1}=1\)<=> x=1+1=2

vậy x=2

b) \(\sqrt{x+3}+\sqrt{x-2}=5\) điều kiện \(x\ge2\)

<=> \(x+3+x-2+2\sqrt{\left(x+3\right)\left(x-2\right)}=25\)

<=> \(\sqrt{x^2+x-6}=12-x\)<=> \(x^2+x-6=x^2-24x+144\)

<=> 25x=150=> x=6 ( thỏa) 

vậy x=6