If a2−1a2=5, evaluate a4+1a4a^2 - \dfrac{1}{a^2} = 5, \text{ evaluate } a^4 + \dfrac{1}{a^4}a2−a21=5, evaluate a4+a41.
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We know that,
a4+1a4=(a2−1a2)2+2a^4 + \dfrac{1}{a^4} = \Big(a^2 - \dfrac{1}{a^2}\Big)^2 + 2a4+a41=(a2−a21)2+2
Substituting values we get,
a4+1a4=(5)2+2=25+2=27.a^4 + \dfrac{1}{a^4} = (5)^2 + 2 = 25 + 2 = 27.a4+a41=(5)2+2=25+2=27.
Hence, a4+1a4=27.a^4 + \dfrac{1}{a^4} = 27.a4+a41=27.
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