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) $2$.

Tutorialspoint

Updated on: 10-Oct-2022

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