Question

If x + y = - 4 find the value of x^3 +y^3 -12xy+ 64.

Answer 1

$\sf{Answer}$

Given :-

x + y = -4

To find ;-

x³ + y³ - 12xy + 64 =?

Formula used :-

(x + y)³ = x³ + y³ + 3xy (x + y)

Lets do !

x + y = - 4

Cubing on both sides

( x + y)³ = (-4)³

By using above formula

(x + y)³ = x³ + y³ + 3xy (x + y)

x³ + y³ + 3xy ( x + y) = -64

x³ +y³ + 3xy (-4) = -64

x³ + y³ - 12xy = -64

Transpose 64 To RHS

x³ + y³ - 12xy + 64 = 0

So, Required answer is x³+ y³ - 12xy + 64 = 0

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More identities to learn

( a - b)³ = a³ - b³ -3ab ( a-b)

a³ + b³ = (a + b)³ -3ab

a² + b² = (a+b)² -2ab

2a² + 2b² = (a+b)² + (a -b)²

(a+b) (a-b) = a²-b²

( a + b)² = a²+b² +2ab

(a -b)² = a²+b² -2ab

( a + b + c)² = a²+b²+c²+2ab+2bc+2ca

a + b + c = 0 then a³+b³+c³ = 0