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UPSC CDS 1 2022 Math Paper

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Question : 6 of 100

Marks: +1, -0

What is the value of the following?

\frac{(5.4)^{3} - 0.064}{(5.4)^{2} + 2.16 + 0.16}

4
4.4
5
5.4

Solution:

Concept:

The expression matches the algebraic identity

a^3 - b^3 = (a-b)(a^2+ab+b^2)

, which allows cancellation of the common factor.

Explanation:

Let

a = 5.4

and

b = 0.4

.

Then

b^3 = 0.064

,

ab = 5.4 \times 0.4 = 2.16

, and

b^2 = 0.16

.

Thus the numerator

(5.4)^3 - 0.064

becomes

a^3 - b^3

.

The denominator

(5.4)^2 + 2.16 + 0.16

becomes

a^2 + ab + b^2

.

Using the identity:

\frac{a^3 - b^3}{a^2 + ab + b^2} = a - b

.

Substitute the values:

5.4 - 0.4 = 5

.

Answer:

5

(Option C).

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