যদি a-(1/a) = 2 হয়, তবে a⁴+(1/a⁴) = কত?
Solution
Correct Answer: Option C
a - (1/a) = 2
a + (1/a) = √(a - 1/a)^2 + 4.a. 1/a
= √(2)^2 + 4
= √8
= 2√2
a⁴+(1/a⁴) = (a^2)^2 + (1/a^2)^2
= (a^2+1/a^2)^2 - 2.a^2.1/a^2
= {(a)^2+ (1/a)^2}^2 - 2
= {(a+1/a)^2 - 2.a. 1/a}^2 - 2
= {(2√2)^2 - 2}^2 - 2
= (8 - 2)^2 - 2
= 36 - 2
= 34
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