# 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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