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

English

Gujarati

Hindi

Basic of Logarithms

medium

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

Share

Similar Questions

If ${x^y} = {y^x},$then ${(x/y)^{(x/y)}} = {x^{(x/y) – k}},$ where $k = $

medium

If ${a^{1/x}} = {b^{1/y}} = {c^{1/z}}$ and ${b^2} = ac$ then $x + z = $

easy

The square root of $\sqrt {(50)} + \sqrt {(48)} $ is

medium

${{3\sqrt 2 } \over {\sqrt 6 + \sqrt 3 }} – {{4\sqrt 3 } \over {\sqrt 6 + \sqrt 2 }} + {{\sqrt 6 } \over {\sqrt 3 + \sqrt 2 }} = $

easy

Solution of the equation $\sqrt {(x + 10)} + \sqrt {(x – 2)} = 6$ are

medium