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Multiple Choice Questions

If x2 y2 1 2x then the value of x3 y5 is ........

Quantitative Aptitude (CPO) Algebra

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If x² + y² + 1 = 2x, then the value of x³ + y⁵ is

-1

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Explanation:

x² + y² + 1 = 2x
⇒ x² + y² + 1 – 2x = 0
⇒ x² – 2x + 1 + y² = 0
⇒ (x – 1)² + y² = 0
In the above eq. the L.H.S. can only become zero when the base of terms; (x – 1)and y becomes zero because for any other value the sum of their squares will always be a positive integer.
Taking (x – 1) = 0
and y = 0
Therefore, x = 1 and y = 0
∴ x³ + y⁵ = 1 + 0 = 1.