Express $17^2$ as the sum of two consecutive number.

To do: To express $17^2$ as the sum of two consecutive positive integers.

Solution:

Let $x$ and $( x+1)$ be the first integer and second integer respectively whose sum is equal to $17^{2}=289$.

$\Rightarrow x+x+1=289$

$\Rightarrow 2x+1=289$

$\Rightarrow 2x=288$

$\Rightarrow x=\frac{288}{2}$

$\Rightarrow x=144$

Therefore, first integer$=x=144$ and second integer$=x+1=144+1=145$.

Thus, $17^2=144+145$

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Updated on: 10-Oct-2022

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