If x = a1 / 3 + a-1 / 3 , y = a1 / 2

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If x = a^{1 / 3} + a^{-1 / 3} , y = a^{1 / 2} - a^{-1 / 2} then value of (x⁴ - x²y² – 1) + (y⁴ - x²y² + 1) is

1. 16
2. 13
3. 12
4. 14

Correct Option: A

x = a^{1 / 3} + a^{-1 / 3}
y = a^{1 / 2} - a^{-1 / 2}
∴ x² – y² = 4a^{1 / 2}.a^{-1 / 2} = 4
[∴ (a + b)² – (a – b)² = 4ab]
Again, y² - x² = -4a^{1 / 2}.a^{-1 / 2} = -4
Expression = (x⁴ - x²y² – 1) + (y⁴ - x²y² + 1)
Expression = x²(x² - y²) – 1 + y²(y² - x²) + 1
Expression = 4x² - 1 - 4y² + 1
Expression = 4(x² - y²) = 4 × 4 = 16