Question 104

What is the value of $$\frac{(0.5^{3})-(0.1)^{3}}{(0.5)^{2}+0.5 \times 0.1+(0.1)^{2}}$$?

Solution

Given $$\frac{(0.5^{3})-(0.1)^{3}}{(0.5)^{2}+0.5 \times 0.1+(0.1)^{2}}$$......(1)

we know that $$a^{3} - b^{3} = (a - b) (a^{2} + ab + b^{2})$$......(2)

Substitute (2) in (1)

$$\frac{(0.5-0.1)(0.5)^{2} + 0.5 \times 0.1 + (0.1)^{2}}{(0.5)^{2}+0.5 \times 0.1+(0.1)^{2}}$$

$$0.5 - 0.1 = 0.4$$

Hence, option B is the correct answer.

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