107 × 107+93 × 93= ? · ABC26GN0176
Subject: General Aptitude · Chapter: Number System
$107 \times 107+93 \times 93=$ ?
(a)19578
(b)19418
(c)20098
(d)21908
(e)None of these
Answer
Explanation
$$\begin{aligned} (107 \times 107)+(93 \times 93) & =(107)^{2}+(93)^{2} \\ & =(100+7)^{2}+(100-7)^{2} \\ & =(a+b)^{2}+(a-b)^{2}=2\left(a^{2}+b^{2}\right) \\ & =2\left[(100)^{2}+7^{2}\right]=2[10000+49] \\ & =2 \times 10049=20098 . \end{aligned}$$
Explanation as extracted from the printed page; notation may be imperfect.
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