Question

if 2x+3y=6,xy=12 find the value of8x3+27y3​

Answer 1

Hey MATE!!

We are given that,

2x +3y =6 ---1equation

and xy =12---2nd equation

We have to find,

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

So 1st we take cube on both sides of equation 1st:

(2x +3y) ^3 = 6^3

Applying (a+b)^3 = a^3 +b^3 +3(a^2)b +3a(b^2)

=> (2x)^3 + (3y)^3 + 3(2x)^2(3y) + 3(2x)(3y) ^2 = 216

=> 8x^3 + 27y^3 + 36x^2+ 54xy^2 = 216

=> 8x^3 + 27y^3 + 36(xy)(x) + 54(xy)(y) = 216

=> 8x^3 + 27y^3 + 36(12)x + 54(12)y = 216

=> 8x^3 + 27y^3 + 437x + 648y = 216

Hence,

8x^3 + 27y^3 = 216 - (437x + 648y)

This is the only final conclusion of the question since no other information is given to solve for x and y. If you still have doubts then inbox is open for help.

Hope it helps

HAKUNA MATATA :))