Find the value of $$\frac{\left( (3.17 + 9.12)^2 + (3.17 - 9.12)^2 \right)}{(3.17 \times 3.17 + 9.12 \times 9.12)}$$​

Correct option is A

Formula Used:

​$$(A+B)^2= A^2+B^2+2AB\\(A-B)^2= A^2+B^2-2AB$$​​
Solution:
​$$\frac{\left( (3.17 + 9.12)^2 + (3.17 - 9.12)^2 \right)}{(3.17 \times 3.17 + 9.12 \times 9.12)} \\\ \\= \frac{\left( (3.17 + 9.12)^2 + (3.17 - 9.12)^2 \right)}{3.17 \times 3.17 + 9.12 \times 9.12} \\\ \\= \frac{[(3.17)^2 + (9.12)^2+ 2\times 3.17 \times 9.12] +[(3.17)^2 + (9.12)^2-2\times 3.17 \times 9.12] }{3.17 \times 3.17 + 9.12 \times 9.12} \\\ \\= \frac{2[(3.17)^2 + (9.12)^2]}{3.17 \times 3.17 + 9.12 \times 9.12} \\\ \\= \frac{2[(3.17)^2 + (9.12)^2]}{[(3.17)^2 + (9.12)^2]} \\\ \\= 2$$​​