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Solve (√x/√(1-x))+√(1-x)=5/2?

Raunak Sarkar , 12 Years ago

Grade 10

1 Answers

Arun Kumar

Last Activity: 10 Years ago

Hi
$\\\frac{\sqrt{x}}{\sqrt{1-x}}+\sqrt{1-x}=5/2 \\x=cos^2x$ seeing $0<x<1 \\tan{x}=5/2-sinx \\=>tan^2x=(5/2-sinx)^2 \\=>sec^2-1=(5/2-sinx)^2 \\=>\frac{1}{1-sin^2}-1=(5/2-sinx)^2 \\=>\frac{sin^2x}{1-sin^2}=(\frac{5}{2}-sinx)^2$
$\\sin^2x=(1-sin^2x)(5/2-sinx)^2 \\=>sin^2x=(1-sin^2x)(25/4-5sinx+sin^2x) \\=>sin^2x=25/4-5sinx-21/4sin^2x+5sin^3x-sin^4x \\=>25/4-5sinx-25/4sin^2x+5sin^3x-sin^4x=0 \\=>sin^4x-5sin^3x+25/4sin^2x+5sinx-25/4=0$
Apprarently its not possbible to solve this quadratic equation under JEE methods.

Arun Kumar, Btech, IIT delhi, Askiitians Faculty

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