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Without actually calculating the cubes, find the value of : (0.2)³ - (0.3)³ + (0.1)³

Solution:

Given, the expression is (0.2)³ - (0.3)³ + (0.1)³

We have to find the value of the expression without actually calculating the cubes.

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 = 0.2; y = -0.3; z = 0.1

x + y + z = 0.2 - 0.3 + 0.1

= 0.3 - 0.3

= 0

x + y + z = 0

Hence, x³ + y³ + z³ = 3xyz.

3xyz = 3(0.2)(-0.3)(0.1)

= (0.6)(-0.03)

= -0.018

Therefore, (0.2)³ - (0.3)³ + (0.1)³ = -0.018.

✦ Try This: Without actually calculating the cubes, find the value of : (2)³ + (3)³ - (5)³

☛ Also Check: NCERT Solutions for Class 9 Maths Chapter 2

NCERT Exemplar Class 9 Maths Exercise 2.3 Problem 37(ii)

Summary:

Without actually calculating the cubes, the value of (0.2)³ - (0.3)³ + (0.1)³ is -0.018

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