Question

If, x+y+4=0, then what's the value of x³+y³-12xy+64?​

Answer 1

Answer :-

Given :-

• x + y + 4 = 0

To Find :-

• Value of x³ + y³ - 12xy + 64

Solution :-

Identity used :-

If a + b + c = 0

• a³ + b³ + c³ = 3abc

= x³ + y³ - 12xy + 64

= ( x )³ + ( y )³ + ( 4 )³ - 12xy

Here, as x + y + 4 = 0. So,

• x³ + y³ + 4³ = 3 × x × y × 4 = 12xy

= 12xy - 12xy

= 0

Value of x³ + y³ - 12xy + 64 = 0

Additional information :-

(a + b)² = a² + 2ab + b²

(a - b)² = a² - 2ab + b²

(a + b + c)² = a² + b² + c² + 2(ab + bc + ca)

(a + b)³ = a³ + b³ + 3ab(a + b)

(a - b)³ = a³ - 3a²b + 3ab² - b³

a³ + b³ = (a + b)( a² - ab + b² )

a³ - b³ = (a - b)( a² + ab + b²)