If x4 + 1/x4 = 257/16 then find 8/13 
where x > 0.
Show answer & explanation
Correct answer: D
Explanation
The correct answer is option 4 i.e 5
| Understanding | Application |
| We will use the identity of (a + b)2 to solve the algebraic equation. |
We have given that, ⇒ x4 + 1/x4 = 257/16 Adding two in both the sides ⇒ x4 + 1/x4 + 2 = 257/16 + 2 ⇒ (x2 + 1 / x2)2 = 289 / 16 ⇒ x2 + 1 / x2 = 17 / 4 Adding two in both sides of the equation, ⇒ x2 + 1 / x2 + 2 = 17 / 4 + 2 ⇒ (x + 1 / x)2 = 25 / 4 ⇒ x + 1 / x = 5 / 2 ⇒ (x + 1 / x)3 = x3 + 1 / x3 + 3(x + 1 / x) ⇒ 125 / 8 = x3 + 1 / x3 + 3(5 / 2) ⇒ x3 + 1 / x3 = 125 / 8 - 15 / 2 = 65 / 8 ⇒ (8 / 13) × 65 / 8 = 5 |