Question

If 2x+3y= 13 and xy= 6 find the value of 8x cube + 27y cube

Answer 1

8x³+27y³
=(2x)³+(3y)³
=(2x+3y)³-3(2x)(3y)(2x+3y)
=(13)³-3(6xy)(13)
=2197-36(6×6)
=2167-36(36)
=2167-1296
=871

Answer 2

Step-by-step explanation:

Given :

2x + 3y = 13 and xy = 6

To find :

value of 8x³ + 27y³

 

Solution :  

By using the identity, (a + b)³ = a³ + b³ + 3ab(a + b)  

On cubing 2x + 3y = 13 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 x 6 x 13 = 2197

8x³ + 27y³ + 1404 = 2197

8x³ + 27y³ = 2197 – 1404  

8x³ + 27y³ = 793

Hence the value of  8x³ + 27y³ is  793.