Question : What is the value of $\frac{(0.91)^3+(0.09)^3}{ [(0.91)^2-0.0819+(0.09)^2]}$?
Option 1: 1
Option 2: 5
Option 3: 4
Option 4: 6
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Correct Answer: 1
Solution :
Using $(a^3+b^3)=(a+b)(a^2+b^2-ab)$
$\frac{(0.91)^3+(0.09)^3}{ [(0.91)^2-0.0819+(0.09)^2]}$
= $\frac{(0.91+0.09)[(0.91)^2-0.0819+(0.09)^2]}{ [(0.91)^2-0.0819+(0.09)^2]}$
= 0.91 + 0.09
= 1
Hence, the correct answer is 1.
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