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The equation root(x+1) - root(x-1) = root(4x-1) has how many solutions?

The equation
root(x+1) - root(x-1) = root(4x-1) has how many solutions?

Grade:11

1 Answers

Rinkoo Gupta
askIITians Faculty 81 Points
10 years ago
root (x+1) -root(x-1)=root(4x-1)
squaring both sides, we get
x+1+x-1-2root(x^2-1)=4x-1
2x-2root(x^2-1)=4x-1
-2x+1=2root(x^2-1)
squaring again both sides
4x^2+1-4x=4(x^2-1)
4x^2+1-4x=4x^2-4
5=4x
x=5/4
Thanks & Regards
Rinkoo Gupta
AskIITians Faculty

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