Solve this: Q 12 If 2x - 3y = 10 and xy = 16; find the value of 8x3-27y3 - Maths - Expansions

Question

Solve this:
Q 12 If 2x - 3y = 10 and xy = 16; find the value of 8 x 3 - 27 y
3

Jegannathan Anandaraman · Accepted Answer

Hello Divyansh, given 2x - 3y = 10 and x y = 16
We need 8x^3 - 27 y^3
==> (2x)^3 - (3y)^3 = ( 2x - 3y) ( 4x^2 + 9y^2 + 6 xy)
Now we need 4x^2 + 9 y^2
So let us follow this way
(2 x - 3y)^2 = 4x^2 + 9y^2 - 12 xy
==> 100 = 4 x^2 + 9y^2 - 12 * 16
So 4 x^2 + 9 y^2 = 100 + 192 = 292
Now let us go to the beginging status
8x^3 - 27y^3 = 10 (292 + 96) = 3880

Solve this: Q.12. If 2x - 3y = 10 and xy = 16; find the value of 8 x 3 - 27 y 3 .

Solve this:
Q.12. If 2x - 3y = 10 and xy = 16; find the value of $8 x^{3} - 27 y^{3}$ .