Question
Download Solution PDFIf 2x + 3y = 16 and xy = 9, then find 8x3 + 27y3
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:-
2x + 3y = 16 and xy = 9
Concept used:-
(a + b)3 = a3 + b3 + 3ab(a + b)
Calculation:-
a3 + b3 = (a + b)3 - 3ab(a + b)
8x3 + 27y3
⇒ (2x)3 + (3y)3
⇒ (2x + 3y)3 - 3 × 2x × 3y (2x + 3y)
⇒ (2x + 3y)3 - 18xy (2x + 3y)
⇒ 163 - 18 × 9 × 16
⇒ 4096 - 2592
⇒ 1504
∴ The required answer is 1504.
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