Question : If $a-b=1$ and $a^{3}-b^{3}=61$, then the value of $ab$ will be:
Option 1: –20
Option 2: 20
Option 3: 30
Option 4: 60
Answer (1)
19th Jan, 2024
Correct Answer: 20
Solution :
Given: $a-b=1$ and $a^{3}-b^{3}=61$
$\therefore a^3–b^3=(a–b)^3+3ab(a–b)$
Putting the values, we get
⇒ $61 = 1 + 3ab × 1$
⇒ $61 – 1 = 3ab$
⇒ $3ab= 60$
Thus, $ab=\frac{60}{3}=20$
Hence, the correct answer is 20.
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