Question

Find the value of x³ + y³ - 12xy + 64 when x + y = - 4

Answer 1

x³ + y³ - 12xy + 64
x³ + y³ + 4³ - 3(4xy)       (64 = 4³)
(x + y + 4)(x² + y² + 4²  - xy - 4y - 4x)
x + y = - 4
(- 4 + 4) * (x² + y² + 4²  - xy - 4y - 4x)
0 * (x² + y² + 4²  - xy - 4y - 4x)
= 0

Answer 2

Given,

x³ + y³ - 12xy + 64

x + y = - 4

To find,

The value of x³ + y³ - 12xy + 64.

Solution,

The value of x³ + y³ - 12xy + 64 will be 0.

We can easily solve this problem by following the given steps.

According to the question,

x³ + y³ - 12xy + 64

This expression can be re-written as follows:

(x)³ + (y)³ + (4)³ - 3(x)(y)(4)

Now, if we observe this expression very carefully we find that it can be solved using the identity, a³ + b³ + c³ -3abc = (a+b+c) ( a² + b² + c² - ab - bc - ca)

In this case, a = x, b = y and c = 4.

Now, using this identity,

x³ + y³ - 12xy + 64 = (x+y+4) (x² +y²+4²-xy-4y-4x)

Putting the value of (x+y) in this expression,

(-4+4) (x² +y²+4²-xy-4y-4x)

0 × (x² +y²+4²-xy-4y-4x)

0

( Note that if we multiply any number with zero then the result will always be zero.)

Hence, the value of x³ + y³ - 12xy + 64 is 0.