Find the value of x³ - 8y³ - 36xy - 216, when x = 2y + 6
Solution:
Given, x = 2y + 6
We have to find the value of x³ - 8y³ - 36xy - 216.
The expression can be rewritten as x - 2y - 6 = 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 = -2y and c = -6
a³ + b³ +c³ = 3abc = 3(x)(-2y)(-6)
x³ - 8y³ + (-6)³ = 36xy
The expression can be rewritten as x³ + y³ - 12xy + (4)³
= x³ - 8y³ - (6)³ - 36xy
Substituting the value of x³ - 8y³ - (6)³,
= 36xy - 36xy
= 0
Therefore, the value of x³ - 8y³ - 36xy - 216 is 0.
✦ Try This: If x - 1/x = 2, 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(ii)
Find the value of x³ - 8y³ - 36xy - 216, when x = 2y + 6
Summary:
The value of x³ - 8y³ - 36xy - 216 using the algebraic identity, when x = 2y - 6 is 0
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