ABC26GN0177 · Number System
Subject: General Aptitude · Chapter: Number System · Exam: · Marks: · Difficulty:
$217 \times 217+183 \times 183=$ ?
(a)79698
(b)80578
(c)80698
(d)81268
(e)None of these
Answer
Explanation
$$\begin{aligned} (217 \times 217) & +(183 \times 183)=(217)^{2}+(183)^{2} \\ & =(200+17)^{2}+(200-17)^{2}=(a+b)^{2}+(a-b)^{2} \\ & =2\left(a^{2}+b^{2}\right), \text { where } a=200, b=17 \\ & =2\left[(200)^{2}+(17)^{2}\right]=2[40000+289] \\ & =(2 \times 40289)=80578 . \end{aligned}$$
Explanation as extracted from the printed page; notation may be imperfect.
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