2018 · Q11
If x⁶ + 1/x⁶ = k(x² + 1/x²), then k is equal to
Elementary MathematicsAlgebra
- Ax² − 1 + 1/x²
- Bx⁴ − 1 + 1/x⁴
- Cx⁴ + 1 + 1/x⁴
- Dx⁴ − 1 − 1/x⁴
Explanation
Put y = x^2 + 1/x^2. Then x^6 + 1/x^6 = (x^2)^3 + (1/x^2)^3 = y^3 - 3y. So k = y^2 - 3 = (x^2 + 1/x^2)^2 - 3 = x^4 + 2 + 1/x^4 - 3 = x^4 - 1 + 1/x^4. Hence option B.