Select the correct answerThe difference between the squares of two consecutive numbers is 35. The numbers are?Options18&1717&1816&1819&2017&20

Break Down the Problem

1. Let the two consecutive numbers be $n$ and $n+1$.
2. We need to find the difference between their squares: $(n+1)^2 - n^2 = 35$.

Relevant Concepts

1. The difference of squares can be expressed as: $(a+b)(a-b)$ For our problem, this translates to: $(n+1+n)(n+1-n) = 35 \quad \text{or} \quad (2n+1)(1) = 35.$
2. This simplifies to $2n + 1 = 35$.

Analysis and Detail

1. To find $n$: $2n + 1 = 35$ Subtract 1 from both sides: $2n = 34$ Divide by 2: $n = 17.$
2. Thus, the two consecutive numbers are $n = 17$ and $n + 1 = 18$.

Verify and Summarize

1. Calculate the difference of squares: $18^2 - 17^2 = 324 - 289 = 35.$
2. The calculation is verified.

Final Answer

The two consecutive numbers are 17 and 18.