Question : Simplify: $\frac{(612+388)^2+(612-388)^2}{(612 \times 612)+(388 \times 388)}=?$
Option 1: 1
Option 2: 4
Option 3: 2
Option 4: 3
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Correct Answer: 2
Solution :
Given: $\frac{(612+388)^2+(612-388)^2}{(612 \times 612)+(388 \times 388)}$
$= \frac{(612)^2 + (388)^2 +2 \times 612 \times 388 + (612)^2 + (388)^2 -2 \times 612 \times 388}{(612)^2 + (388)^2 }$
$= \frac{2[(612)^2 + (388)^2 ]}{(612)^2 + (388)^2 }$
$= 2$
Hence, the correct answer is 2.
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