If 2x+3y=13 and xy=6, find the value of 8x3+27y3.
2x + 3y = 13, xy = 6
Cubing both sides,
(2x+3y)3=(13)3⇒ (2x)3+(3y)3+3×2x×3y(2x+3y)=2197⇒ 8x3+27y3+18xy(2x+3y)=2197⇒ 8x3+27y3+18×6×13=2197⇒ 8x3+27y3+1404=2197⇒ 8x3+27y3=2197−1404=793 ∴ 8x3+27y3=793
If 2x+3y=13 and xy=6 find the value of 8x3+27y3.
If 2x−3y = 10 and xy=16; find the value of 8x3−27y3