Question
Download Solution PDFIf x + y = 36, then find (x - 27)3 + (y - 9)3.
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
x + y = 36
Formula used:
a3 + b3 = (a + b)(a2 - ab + b2)
Calculation:
⇒ x + y = 36
⇒ x + y - 36 = 0 ................(1)
⇒ (x - 27) + (y - 9) = 0
Let consider (x - 27) = a and y - 9 = b.
a3 + b3 = (a + b)(a2 + b2 - ab) using the formula, substitute the value of a and b
into the equation.
⇒ (x - 27)3 + (y - 9)3 = ( x - 27 + y - 9)((x - 27)2 - (x - 27)(y - 9) + (y - 9)2)
⇒ (x - 27)3 + (y - 9)3 = ( x + y - 36)((x - 27)2 - (x - 27)(y - 9) + (y - 9)2)
The value of x + y - 36 = 0 from the equation (1).
⇒ (x - 27)3 + (y - 9)3 = (0)((x - 27)2 - (x - 27)(y - 9) + (y - 9)2)
⇒ (x - 27)3 + (y - 9)3 = 0
∴ The required value is 0.
Last updated on Jul 9, 2025
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