Question : If $a+b=10$ and $ab=6$, then the value of $a^3+b^3$ is:
Option 1: 800
Option 2: 820
Option 3: 860
Option 4: 840
Answer (1)
25th Jan, 2024
Correct Answer: 820
Solution :
According to the question,
$a + b$ = 10 and $ab$ = 6
⇒ $(a + b)^{2}$ = 102
⇒ $a^{2} + 2ab + b^{2}$ = 100
⇒ $a^{2} + 2(6) + b^{2}$ = 100
⇒ $a^{2} + 12 + b^{2}$ = 100
⇒ $a^{2} + b^{2}$ = 88
Now,
⇒ $a^{3} + b^{3} = (a + b)(a^{2} − ab + b^{2})=(10)(88 − 6)=10 × 82$ = 820
Hence, the correct answer is 820.
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