Question : What is the value of $\small \frac{(0.7)^{3}-(0.4)^{3}}{(0.7)^{2}+0.7\times 0.4+(0.4)^{2}}$?
Option 1: 0.3
Option 2: 0.7
Option 3: 0.9
Option 4: 1.1
Answer (1)
6th Jan, 2024
Correct Answer: 0.3
Solution :
Consider, $\frac{(0.7)^{3}-(0.4)^{3}}{(0.7)^{2}+0.7\times 0.4+(0.4)^{2}}$
We know, $a^3-b^3=(a-b)(a^2+ab+b^2)$
$=\frac{(0.7-0.4)((0.7)^{2}+0.7\times 0.4+(0.4)^{2})}{(0.7)^{2}+0.7\times 0.4+(0.4)^{2}}$
$=0.7 - 0.4$
$= 0.3$
Hence, the correct answer is 0.3.
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