Question : $\frac{3.25\times 3.25+1.75\times 1.75-2\times 3.25\times 1.75}{3.25\times 3.25-1.75\times 1.75}$ is simplified to:
Option 1: 0.5
Option 2: 0.4
Option 3: 0.3
Option 4: 0.2
Correct Answer: 0.3
Solution :
Consider, $\frac{3.25\times 3.25+1.75\times 1.75-2\times 3.25\times 1.75}{3.25\times 3.25-1.75\times 1.75}$
$=\frac{(3.25)^2+(1.75)^2-2\times 3.25\times1.75}{(3.25)^2-(1.75)^2}$
Using $a^2+b^2-2ab = (a-b)^2$ and $a^2-b^2=(a-b)(a+b)$, we get,
$=\frac{(3.25-1.75)^2}{(3.25-1.75)(3.25+1.75)}$
$=\frac{3.25-1.75}{3.25+1.75}$
$=\frac{1.5}{5}$
$= 0.3$
Hence, the correct answer is 0.3.
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