Question:
If \((a – b) = 6\) and \((a^3 – b^3) = 936\), then find the value of \((a \times b)\).
यदि \((a – b) = 6\) और \((a^3 – b^3) = 936\) है, तो \((a \times b)\) का मान ज्ञात कीजिए।
Options:
- 35
- 36
- 38
- 40
- 35
- 36
- 38
- 40
Correct Answer: d)
Explanation:
Using the algebraic identity:
\(a^3 – b^3 = (a – b)^3 + 3ab(a – b)\)
\(936 = 6^3 + 3ab(6) \implies 936 = 216 + 18ab\)
\(18ab = 936 – 216 = 720 \implies ab = \dfrac{720}{18} = 40\).
बीजगणितीय सर्वसमिका का प्रयोग करने पर:
\(a^3 – b^3 = (a – b)^3 + 3ab(a – b)\)
\(936 = 6^3 + 3ab(6) \implies 936 = 216 + 18ab\)
\(18ab = 936 – 216 = 720 \implies ab = \dfrac{720}{18} = 40\)।