Algebra

Quantitative Aptitude (CPO)

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If x + y = 15, then (x – 10)³ + (y – 5)³ is

125

625

Explanation:

Given, x + y = 15
∴ (x – 10)³ + (y – 5)³
We can express it in the form of
a³ + b³ = (a + b)³ – 3ab(a + b)
(x – 10)³ + (y – 5)³ = (x – 10 + y – 5)³ – 3(x – 10)(y – 5)(x – 10 + y – 5)
⇒ (x + y – 15)³ – 3(x – 10)(y – 5)(x + y – 15) = 0
Putting the value of x + y, we get
⇒ (15 – 15)³ – 3(x – 10)(y – 5)(15 – 15)
⇒ (0)³ – 3(x – 10)(y – 5)(0) = 0.

By: Amit Kumar

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