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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