COMEDK · Maths · 17. Mathematical Reasoning
If \(a \mid(b+c)\) and \(a \mid(b-c)\), where \(a, b, c \in N\), then
- A \(c^{2} \equiv a^{2}\left(\bmod b^{2}\right)\)
- B \(a^{2} \equiv b^{2}\left(\bmod c^{2}\right)\)
- C \(a^{2}+c^{2}-b^{2}\)
- D \(b^{2} \equiv c^{2}\left(\bmod a^{2}\right)\)
Answer & Solution
Correct Answer
(D) \(b^{2} \equiv c^{2}\left(\bmod a^{2}\right)\)
Step-by-step Solution
Detailed explanation
\(b \equiv c(\bmod a)\) So, \(\frac{b+c}{a}\) and \(\frac{b-c}{a}=\frac{(b+c)(b-c)}{a^{2}}\) \(=\frac{b^{2}-c^{2}}{a^{2}} \text { or } \frac{a^{2}}{b^{2}-c^{2}}\) Here, \(b^{2} \equiv c^{2}\left(\bmod a^{2}\right)\)
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