Find the Value of X3 + Y3 − 12xy + 64, When X + Y =−4 - Mathematics

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

Solution

The given expression is

x^3 +y^3 - 12xy +64

It is given that

x+y = -4

⇒ x+y+4 = 0

The given expression can be written in the form

x^3+y^3 -12xy +64 = x^3 +y^3+ 64 -12xy

 = (x)^3 + (y)^3 + (4)^3 - 3.(x).(y).(4)

Recall the formula

a^3+b^3 +c^3 -3abc = (a+b+c)(a^2+b^2 +c^2 - ab -bc - ca)

Using the above formula, we have

x^3 +y^3 -12xy +64

= (x+y+4){(x)^2 + (y)^2 + (4)^2 - (x).(y) - (y).(4) -(4).(x)}

 = (x+y+4)(x^2 +y^2 +16 - xy -4y -4x)

 = 0.(x^2 +y^2 +16 - xy -4y-4x)

 = 0

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APPEARS IN

RD Sharma Mathematics for Class 9
Chapter 5 Factorisation of Algebraic Expressions
Exercise 5.4 | Q 16 | Page 23