Without actually calculating the cubes, find the value of : (1/2)³ + (1/3)³ - (5/6)³
Solution:
Given, the expression is (1/2)³ + (1/3)³ - (5/6)³
We have to find the value of the expression without actually calculating the cubes.
Using the algebraic identity,
x³ + y³ + z³ - 3xyz = (x + y + z) (x² + y² + z² - xy - yz - zx)
If x + y + z = 0, then x³ + y³ + z³ - 3xyz = 0
So, x³ + y³ + z³ = 3xyz.
Here, x = 1/2; y = 1/3; z = -5/6
x + y + z = 1/2 + 1/3 - 5/6
= (2+3)/6 - 5/6
= 5/6 - 5/6
= 0
x + y + z = 0
Hence, x³ + y³ + z³ = 3xyz.
3xyz = 3(1/2)(1/3)(-5/6)
= (1/2)(-5/6)
= -5/12
Therefore, (1/2)³ + (1/3)³ - (5/6)³ = -5/12.
✦ Try This: Without actually calculating the cubes, find the value of : (15)³ + (10)³ - (25)³
☛ Also Check: NCERT Solutions for Class 9 Maths Chapter 2
NCERT Exemplar Class 9 Maths Exercise 2.3 Problem 37(i)
Without actually calculating the cubes, find the value of : (1/2)³ + (1/3)³ - (5/6)³
Summary:
Without actually calculating the cubes, the value of (1/2)³ + (1/3)³ - (5/6)³ is -5/12
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