Question

Giải phương trình: giúp với mik ddag rất cần

a)\(\sqrt{2+\sqrt{x}}\)=3

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

Answer 1

$\sqrt{2+\sqrt{x}}$=3

<=> 2+√x=9

<=> \(\sqrt{x}\)=7

<=> x=49

Answer 2

b) \(\sqrt{2x-2\sqrt{2x-1}}=2\\ < =>2x-2\sqrt{2x-1}=4\)

\(< =>2\sqrt{2x-1}=2x-4\\ < =>2\sqrt{2x-1}=2\left(x-2\right)\)

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

\(< =>2x-1=\left(x-2\right)^2\\ < =>2x-1=x^2-4x+4\)

\(< =>2x-1-x^2+4x-4=0\)

<=> -\(x^2\)+6x-5=0

<=> -(\(x^2\)-6x+5)=0

<=> \(x^2\)-6x+5=0

<=> \(x^2\)-x-5x+5=0

<=> (x-1)(x-5)=0

<=> x=1 hoặc x=5