Question

(a+1/a)²+(a-1/a)².solution​

Answer 1

Hope it helps...

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Answer 2

Answer:

Answer:

As, (a+b)²=a²+2ab+b²

(a–b)²=a²–2ab+b²

$\sf \: ( a + \frac{1}{a} )^{2} - (a - \frac{1}{a} )^{2}$

$\sf \implies \bigg [\frac{a ^{2} + 1}{a} \bigg] {}^{2} - \bigg[\frac{a {}^{2} - 1}{a} \bigg] {}^{2}$

$\sf \implies \bigg [\frac{(a {}^{2} + 1) {}^{2} }{a {}^{2} } \bigg] \bigg [ \frac{ ({a}^{2} + 1) {}^{2} }{a {}^{2} } \bigg] \sf$

[] \sf \implies

$\sf \implies\sf \: =\frac{a {}^{4} + 2a {}^{2} + 1}{a {}^{2} } - \bigg[ \frac{a {}^{4} - 2a {}^{2} + 1 }{a {}^{2} } \bigg]$

$= \sf \: \frac{ {a}^{4} + 2a {}^{2} + 1 - {a}^{4} +2a {}^{2} - 1 }{a {}^{2} }\\ \\ \sf \: =\frac{4a {}^{2} }{a {}^{2} }$

= 4

Hence This Is Answer.