Discussion
\(\dfrac{(963+476)^{2}+(963-476)^{2}}{963\times963+476\times476}=\ ?\)
Answer: C
The expression has the form \[\tfrac{2(a^{2}+b^{2})}{a^{2}+b^{2}}=2\] with a = 963 and b = 476, so the value is 2, option C.
1449, 497 and 4 do not come from this identity.
This is the identity \((a+b)^{2}+(a-b)^{2}=2(a^{2}+b^{2})\). With a = 963 and b = 476 the numerator is 2(963 squared + 476 squared) and the denominator is 963 x 963 + 476 x 476, which is the same sum without the 2, so the fraction is exactly 2 without any arithmetic.
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