If x + y = 15 then (x - 10)3 + (y - 5)3 is:
1). 0
2). 25
3). 125
4).
625
x + y = 15
⇒ (x – 10) + (y – 5) = 0 ……..(1)
Given expression is
(x – 10)3 + (y – 5)3
Applying the identity:- a3 + b3 = (a + b)3 - 3ab(a + b)
= {(x – 10) + (y – 5)}3 – 3(x – 10)( y – 5){(x – 10) + ( y – 5)}
Putting the value from eq. 1
= 0 – 3 (x – 10)( y – 5) × 0
= 0