Question

if X + Y = 4,find x³ + y³​

Answer 1

this answer may help you

Answer 2

Heya!

( x³ + y³ ) = ( x + y )³ -3xy ( x + y )

( x + y ) = 4 ...( Give )

xy = ?

WE KNOW THAT A.M ≥ G.M

A.M means Arithmetic mean And

G.M means geometry mean.

( x + y )/2 ≥ ( xy )½

( xy )½ ≤ 2

SQUARING ON BOTH SIDES WE HAVE

(xy) ≤ 4

On taking Maximum value of xy we have xy = 4

So,

( x³ + y³ ) = ( 4 )³ -3 ( 4 ) ( 4 )

( x³ + y³ ) = 64 -48

( x³ + y³ ) = 16