Question
Find the value of $17^3-16^3.$
✓
Answer
We have, $17^3-16^3$
We know that $\text{b}^3-\text{a}^3=1+3 \text{ab,} \text{b}>\text{a},$
where $\text{a}$ and $\text{b}$ are consecutive numbers.
On putting $\text{a}=16$ and $\text{b}=17,$ we get
$17^3-16^3=1+3 \times 16 \times 17=817$
We know that $\text{b}^3-\text{a}^3=1+3 \text{ab,} \text{b}>\text{a},$
where $\text{a}$ and $\text{b}$ are consecutive numbers.
On putting $\text{a}=16$ and $\text{b}=17,$ we get
$17^3-16^3=1+3 \times 16 \times 17=817$
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