Equation √ {(x + 1)} - √ {(x - 1)} = √ {(4x - 1)} , x ∈ R has

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Basic of Logarithms

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The equation $\sqrt {(x + 1)} - \sqrt {(x - 1)} = \sqrt {(4x - 1)} $, $x \in R$ has

A

One solution

B

Two solution

C

Four solution

D

No solution

Solution

(d) Given $\sqrt {(x + 1)} – \sqrt {(x – 1)} = \sqrt {(4x – 1)} $…..$(i)$

Squaring both sides, we get, $ – 2\sqrt {({x^2} – 1)} = 2x – 1$

Squaring again, we get, $x = {5 \over 4},$ which does not satisfy eq. $(i).$

Hence, there is no solution of the given equation.

Standard 11

Mathematics

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