Question

x- 1/x = 1/2 find 4x2 = 4/x2
​

Answer 1

$Given \: x - \frac{1}{x} = \frac{1}{2} \: --(1 )$

$i) x^{2} - \frac{1}{x^{2}} \\= \Big( x - \frac{1}{x}\Big)^{2} + 2 \times x \times \frac{1}{x} \\= \Big( x - \frac{1}{x}\Big)^{2} + 2 \\= \Big(\frac{1}{2}\Big)^{2} + 2 \\= \frac{1}{4} + 2 \\= \frac{1+8}{4} \\= \frac{9}{4}$

/* Multiply both sides of by 4 , we get */

$\implies 4 \times \Big(x^{2} - \frac{1}{x^{2}}\Big) = 4 \times \frac{9}{4}$

$\implies 4x^{2} - \frac{1}{4x^{2}} = 9$

Therefore.,

$\red{ Value \;of \: 4x^{2} - \frac{1}{4x^{2}} }\green {= 9 }$

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