a+1a=3 হলেa4+(1a)4=?
Created: 9 months ago | Updated: 3 months ago
Job Solution Bangladesh Krishi Bank Krishi Bank - Data Entry/Control Operator - 29.10.2010 গণিত
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It is given that a+1a=3
Using identity,
(a+b)2=a2+2ab+b2,
we have
a2+1a2=(a+1a)2−2
⇒ a2+1a2=32−2
⇒ a2+1a2=9−2
⇒ a2+1a2=7

Squaring both sides we get,

(a2+1a2)2=72
⇒ (a2)2+(1a2)2+2(a2)(1a2)=72
⇒ a4+1a4+2=49
⇒ a4+1a4=47

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