If 2x+3y=13 and xy=6 then find the value of . . .

Question : If 2x+3y=13 and xy=6 then find the value of 8x³+27y³. [793]

Doubt by Rishabh

Solution :

2x+3y=13 (Given)

xy=6 (Given)

8x³+27y³

(2x)³+(3y)³

[ Using Identity : (x+y)³=x³+y³+3xy(x+y)
Here x=2x & y=3y]

(2x+3y)³ = (2x)³+(3y)³+3(2x)(3y)(2x+3y)
(2x+3y)³ = 8x³+27y³+18xy(2x+3y)
(13)³=8x³+27y³+18(6)(13)

[∵2x+3y=13, xy=6]

2197=8x³+27y³+1404
2197-1404=8x³+27y³

793=8x³+27y³

8x³+27y³=793