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UPSC CDS 1 2022 Math Paper

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Question : 38 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: 👈: Video Solution

Given:

Expression is

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

Formula used:

a^{3} - b^{3} = (a-b)(a^{2} + a b + b^{2})

Calculation:

We have

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

\Rightarrow \; \frac{(5.4)^{3} - (0.4)^{3}}{(5.4)^{2} + 5.4 \times 0.4 + (0.4)^{2}}

On applying the formula

\Rightarrow \; \frac{(5.4-0.4)[(5.4)^{2} + 5.4 \times 0.4 + (0.4)^{2}]}{(5.4)^{2} + 5.4 \times 0.4 + (0.4)^{2}}

\Rightarrow 5.4 - 0.4 = 5

\therefore

The value of the expression is 5 .

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