Find the value of x³ + y³ - 12xy + 64, when x + y = - 4
Solution:
Given, x + y = -4
We have to find the value of x³ + y³ - 12xy + 64.
The expression can be rewritten as x + y + 4 = 0
Using the algebraic identity,
a³ + b³ + c³ - 3abc = (a + b + c) (a² + b² + c² - ab - bc - ca)
If a + b + c = 0, then a³ + b³ + c³ - 3abc = 0
So, a³ + b³ +c³ = 3abc.
Here, a = x; b = y and c = 4
a³ + b³ +c³ = 3abc = 3(x)(y)(4)
x³ + y³ + (4)³ = 12xy
The expression can be rewritten as x³ + y³ - 12xy + (4)³
= x³ + y³ + (4)³ - 12xy
Substituting the value of x³ + y³ + (4)³,
= 12xy - 12xy
= 0
Therefore, the value of x³ + y³ - 12xy + 64 is 0.
✦ Try This: If x + 1/x = 4, then find the value of x² + 1/x².
☛ Also Check: NCERT Solutions for Class 9 Maths Chapter 2
NCERT Exemplar Class 9 Maths Exercise 2.3 Problem 39(i)
Find the value of x³ + y³ - 12xy + 64, when x + y = - 4
Summary:
The value of x³ + y³ - 12xy + 64, when x + y = - 4 using the algebraic identity is 0
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