Question

Find the value of 8x^3+ 27y^3 if 2x+3y=8 and xy =2

Answer 1

hey friend here is your answer

we know that

a³+b³ = (a+b) (a²+b²-ab)
= (a+b) ((a+b)²-2ab-ab)
= (a+b)((a+b)²-3ab)

Now

8x³+27y³ = (2x)³+(3y)³
= (2x+3y)((2x+3y)²-3×2x×3y)
= (2x+3y)((2x+3y)²-18×xy)
= (8)((8²-18×2)
= 8×(64-36)
= 8×28
= 224________answer

hope it will help..

Answer 2

given 2x+3y=8

on cubing both sides, we get

(2x+3y)^3 = (8)^3

8x^3 +27y^3 +3(2x)(3y)(2x+3y) = 512

8x^3 +27y^3 + 18(xy)(8)= 512

8x^3 + 27y^3 + 18(2)(8)= 512

8x^3 + 27y^3 + 288=512

8x^3 + 27y^3 =224.



hope this helps!