Question

If x+2y=10,xy=15,find x3+8y3

Answer 1

Hi ,

x + 2y = 10 ------( 1 )

xy = 15 -----------( 2 )
_______________________
We know that ,

a³ + b³ + 3ab( a + b ) = ( a + b )³
________________________

Here ,a = x , b = 2y

x³+ (2y)³+3 × x × 2y(x + 2y ) = (x+2y)³

x³ + 8y³ + 6×xy(x+2y) = ( x + 2y )³

x³ + 8y³ = ( x + 2y )³ - 6xy(x + 2y)

= ( 10 )³ - 6 × 15 × 10

[ From ( 1 ) and ( 2 ) ]

= 1000 - 900

= 100

Therefore ,

x³ + 8y³ = 100

I hope this helps you.

:)

Answer 2

Answer:x + 2y = 10 ------( 1 )

xy = 15 -----------( 2 )

_______________________

We know that ,

a³ + b³ + 3ab( a + b ) = ( a + b )³

________________________

Here ,a = x , b = 2y

x³+ (2y)³+3 × x × 2y(x + 2y ) = (x+2y)³

x³ + 8y³ + 6×xy(x+2y) = ( x + 2y )³

x³ + 8y³ = ( x + 2y )³ - 6xy(x + 2y)

= ( 10 )³ - 6 × 15 × 10

[ From ( 1 ) and ( 2 ) ]

= 1000 - 900

= 100

Therefore ,

x³ + 8y³ = 100