Solve:
$ \frac{(946+157)^{2}+(946-157)^{2}}{(946 \times 946+157 \times 157)}=? $
$ (a) 1 $
(b) 2
(c) 789
(d) 1103
Given:
$\frac{(946+157)^{2}+(946-157)^{2}}{(946 \times 946+157 \times 157)}$
To do:
We have to solve the given expression.
Solution:
$\frac{(946+157)^{2}+(946-157)^{2}}{(946 \times 946+157 \times 157)}$
We know that,
$(a+b)^2=a^2+2ab+b^2$ and $(a-b)^2=a^2-2ab+b^2$
Therefore,
$\frac{(946+157)^{2}+(946-157)^{2}}{(946 \times 946+157 \times 157)}=\frac{(946)^2+2(946)(157)+(157)^2+(946)^2-2(946)(157)+(157)^2}{(946 \times 946+157 \times 157)}$
$=\frac{2((946)^2+(157)^2)}{(946 \times 946+157 \times 157)}$
$=2(\frac{946\times946+157\times157}{ 946 \times 946+157 \times 157})$
$=2$
The answer is (b) $2$.
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