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प्रश्न
If a ≠ 0 and `a - 1/a` = 4 ; find : `( a^4 + 1/a^4 )`
उत्तर
`( a - 1/a )^2 = a^2 + 1/a^2 - 2`
⇒ `a^2 + 1/a^2 = ( a - 1/a )^2 + 2`
⇒ `a^2 + 1/a^2 = (4)^2 + 2 [ ∵ a - 1/a = 4]`
⇒ `a^2 + 1/a^2` = 18 ...(1)
We know that,
`a^4 + 1/a^4 = ( a^2 + 1/a^2 )^2 - 2`
= `(18)^2 - 2 [ From(1) ]
= 324 - 2
⇒ `a^4 + 1/a^4 =322`
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