pt<=> \(\dfrac{3\left(2x-1\right)}{\sqrt{x}-\sqrt{1-x}}=3+2\sqrt{x}.\sqrt{1-x}\)
Dat \(\sqrt{x}=a,\sqrt{1-x}=b\)
=> \(2x-1=a^2-b^2\)
pt<=> \(\dfrac{3\left(a^2-b^2\right)}{a-b}=3+2ab\)
=> \(\dfrac{3.\left(a-b\right)\left(a+b\right)}{a-b}=3+2ab\)
=> 3(a+b)=3+2ab
=> 3a+3b=3+2ab
Giải pt
a )\(\sqrt{\dfrac{x-1}{4}}-3=\sqrt{\dfrac{4x-4}{9}}\)
b) \(\sqrt{x^2-4x+4}+\sqrt{x^2+6x+9}=x-3\)
c) \(\sqrt{\dfrac{2x-3}{x-1}}=2\)
Giai pt:
\(\dfrac{6x-3}{\sqrt{x}-\sqrt{1-x}}=3+2\sqrt{x-x^2}\)
giải pt :
a) \(\sqrt{x-1}+\sqrt{x^3+x^2+x+1}=1+\sqrt{x^4-1}\)
b0 \(4\sqrt{x+1}=x^2-5x+14\)
c) \(2x+3\sqrt{4-5x}+\sqrt{x+2}=8\)
d) \(\dfrac{x^2+x}{\sqrt{x^2+x+1}}=\dfrac{2-x}{\sqrt{x-1}}\)
Giải pt:
\(\dfrac{6x^2+4x+8}{x+1}=5\sqrt{2x^2+3}\)
Giải PT: \(\sqrt{1-x}+\sqrt{x^2-3x+2}+\left(x-2\right).\sqrt{\dfrac{x-1}{x-2}}=3\)
Giải pt:
\(\sqrt{x+1+\sqrt{x+\dfrac{3}{4}}}+x=\dfrac{1}{2}\)
Giải pt
\(\sqrt{2x^2+6x-8}+\sqrt{2x^2+4x-6}-3\sqrt{x+4}=3\sqrt{x+3}+1\)
Giải PT: \(\sqrt[4]{\left(x-2\right).\left(4-x\right)}+\sqrt[4]{x-2}+\sqrt[4]{4-x}+6x\sqrt{3x\le x^3+30}\)
giải pt sau
\(\left(\dfrac{\sqrt{x}-1}{x-2\sqrt{x}+1}-\dfrac{2}{\sqrt{x}}\right):\dfrac{2-\sqrt{x}}{x-1}\)
