If x4 - 142x2 + 1 = 0, then the value of x3 + is:
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Correct answer: C
Explanation
The correct answer is option 3 i.e. 1692
(a + b)2 = a2 + b2 + 2ab
(a + b)3 = a3 + b3 + 3ab(a + b)
x4 - 142x2 + 1 = 0
By dividing the equation by x2
⇒ x2 - 142 + 1/x2 = 0
⇒ x2 + 1/x2 = 142
By adding 2 in both LHS & RHS
⇒ x2 + 1/x2 + 2 = 142 + 2
⇒ (x + 1/x)2 = 144
⇒ (x + 1/x) = √144 = 12
By Cubing both sides
⇒ (x + 1/x)3 = 123
⇒ x3 + 1/x3 + 3 × x × 1/x (x + 1/x) = 1728
⇒ x3 + 1/x3 = 1728 - 3 × (x + 1/x) = 1728 - 3 × 12
⇒ x3 + 1/x3 = 1728 - 36 = 1692