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  • If x is a solution of the equation , <img alt="\dpi{100} \sqrt{2x+1}\, -\, \sqrt{2x-1}\, =\, 1,\left ( x\geqslant \frac{1}{2} \right ), then\, \sqrt{4x^{2}-1}" src="https://learn.careers36

If x is a solution of the equation , \dpi{100} \sqrt{2x+1}\, -\, \sqrt{2x-1}\, =\, 1,\left ( x\geqslant \frac{1}{2} \right ), then\, \sqrt{4x^{2}-1}

is equal to :

 

Option: 1

\frac{3}{4}


Option: 2

\frac{1}{2}


Option: 3

2


Option: 4

2\sqrt{2}


Answers (1)

best_answer

\\\sqrt{2x+1}\, -\, \sqrt{2x-1}\, =\, 1\\\Rightarrow \sqrt{2x+1}\, =\, \sqrt{2x-1}\, +\, 1\\\text{square both side}\\\Rightarrow 2x+1=2x-1+1+2\sqrt{2x-1}\\\Rightarrow 1=2\sqrt{2x-1}\\\text{square both side}\\\Rightarrow 2x-1=\frac{1}{4}\\\Rightarrow x=\frac{5}{8}

\text { Now } \sqrt{4 x^{2}-1} \text { at } x=5 / 8 \quad\Rightarrow \quad \sqrt{4 \times \frac{25}{64}-1}=3 / 4

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