Question:
If \(a + b = 18\) and \(a^2 + b^2 = 200\), then find the value of \((a^3 + b^3)\).
यदि \(a + b = 18\) और \(a^2 + b^2 = 200\) है, तो \((a^3 + b^3)\) का मान ज्ञात कीजिए।
Options:
- 3240
- 2484
- 3600
- 3888
- 3240
- 2484
- 3600
- 3888
Correct Answer: b)
Explanation:
We know that:
\((a + b)^2 = a^2 + b^2 + 2ab\)
\(18^2 = 200 + 2ab\)
\(324 = 200 + 2ab \implies 2ab = 124 \implies ab = 62\).
Now, \(a^3 + b^3 = (a + b)(a^2 – ab + b^2)\):
\(a^3 + b^3 = 18 \times (200 – 62) = 18 \times 138 = 2484\).
हम जानते हैं कि:
\((a + b)^2 = a^2 + b^2 + 2ab\)
\(18^2 = 200 + 2ab\)
\(324 = 200 + 2ab \implies 2ab = 124 \implies ab = 62\).
अब, \(a^3 + b^3 = (a + b)(a^2 – ab + b^2)\):
\(a^3 + b^3 = 18 \times (200 – 62) = 18 \times 138 = 2484\)।