Question

Giải phương trình sau:

a)\(\sqrt{3}.x-\sqrt{12}=0\)

b)\(\sqrt{2}.x+\sqrt{2}=\sqrt{8}+\sqrt{18}\)

c)\(\sqrt{5}.x^2-\sqrt{20}=0\)

d)\(\sqrt{x^2+6x+9}=3x+6\)

e)\(\sqrt{x^2-4x+4}-2x+5=0\)

f)\(\sqrt{\dfrac{2x-3}{x-1}=2}\)

g) \(\dfrac{\sqrt{2x-3}}{\sqrt{x-1}}=2\\\)

Answer 1

a) \(\sqrt{3}x-\sqrt{12}=0< =>\sqrt{3}x=\sqrt{12}=>x=2\)

Vay S = { 2 }

b) \(\sqrt{2}x+\sqrt{2}=\sqrt{8}+\sqrt{18}< =>\sqrt{2}x=\sqrt{8}+\sqrt{18}-\sqrt{2}< =>\sqrt{2}x=2\sqrt{2}+3\sqrt{2}-\sqrt{2}\) <=> \(\sqrt{2}x=4\sqrt{2}=>x=4\)

Vay S = { 4 }

c) \(\sqrt{5}x^2-\sqrt{20}=0< =>\sqrt{5}x^2=\sqrt{20}< =>x^2=2=>x=\sqrt{2}\)

Vay S = {\(\sqrt{2}\) }

d) \(\sqrt{x^2+6x+9}=3x+6< =>\sqrt{\left(x+3\right)^2}=3x+6< =>x+3=3x+6< =>-2x=\) \(3=>x=-\dfrac{3}{2}\)

Vay S = { - 3/2 }

e) \(\sqrt{x^2-4x+4}-2x+5=0< =>\sqrt{\left(x-2\right)^2}-2x+5=0< =>x-2-2x+5=0\) <=> \(-x+3=0< =>-x=-3=>x=3\)

Vay S = { 3 }

F) \(\sqrt{\dfrac{2x-3}{x-1}}=2\)

<=> \(\dfrac{2x-3}{x-1}=4< =>2x-3=4x-4< =>-2x=-1=>x=\dfrac{1}{2}\)

Vay S = { 1/2 }

g) \(\dfrac{\sqrt{2x-3}}{\sqrt{x-1}}=2< =>\sqrt{\dfrac{2x-3}{x-1}}=2< =>\dfrac{2x-3}{x-1}=4< =>2x-3=4x-4< =>-2x=-1=>x=\dfrac{1}{2}\)