સમીકરણ $\sqrt {(x + 1)} - \sqrt {(x - 1)} = \sqrt {(4x - 1)} $, $x \in R$ ને .. . .
Medium
Download our app for free and get started
d
(d) Given \(\sqrt {(x + 1)} - \sqrt {(x - 1)} = \sqrt {(4x - 1)} \).....\((i)\)
(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.
Download our appand get started for free
Experience the future of education. Simply download our apps or reach out to us for more information. Let's shape the future of learning together!No signup needed.*
Similar Questions
- 1જો $x + \sqrt {({x^2} + 1)} = a,$ તો $x =$View Solution
- 2${\log _2}7$ એ . . . . થાય.View Solution
- 3${{{x^2} + 1} \over {({x^2} + 4)(x - 2)}}$ ના વિસ્તરણમાં ${x^5}$ નો સહગુણક મેળવો.View Solution
- 4જો ${{{{\sin }^2}x + 1} \over {2{{\sin }^2}x - 5\sin x + 3}}$=${A \over {(2\sin x - 3)}} + {B \over {(\sin x - 1)}} + C$, તોView Solution
- 5જો ${\log _{10}}2 = 0.30103,{\log _{10}}3 = 0.47712$ તો ${3^{12}} \times {2^8}$ માં રહેલા અંકોની સંખ્યા મેળવો.View Solution
- 6જો ${\log _e}\left( {{{a + b} \over 2}} \right) = {1 \over 2}({\log _e}a + {\log _e}b)$, તો $a$ અને $b$ વચ્ચેનો સંબંધ મેળવો.View Solution
- 7${\log _2}.{\log _3}....{\log _{100}}{100^{{{99}^{{{98}^{{.^{{.^{{{.2}^1}}}}}}}}}}}= . . . $.View Solution
- 8$\sqrt {(3 + \sqrt 5 )} = . .$ .View Solution
- 9${{{x^2}} \over {{{(x - 1)}^3}(x - 2)}} = . $. .View Solution
- 10સમીકરણ ${(x)^{x\sqrt x }} = {(x\sqrt x )^x}$ ના ઉકેલની સંખ્યા મેળવો.View Solution