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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


Team Careers360 13th Jan, 2024
Answer (1)
Team Careers360 14th Jan, 2024

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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