Question

the squares of two consecutive integers differ by 23,then find the smallest integer ​

Answer 1

Answer:

Let the required numbers be x and ( x+1).

Atq,

$\: \: \: \: \: \: {(x + 1)}^{2} - {x}^{2} = 23 \\ = > {(x)}^{2} + 2 \times x \times 1 + {(1)}^{2} - {x}^{2} = 23 \\ = > {x}^{2} + 2x + 1 - {x}^{2} = 23 \\ = > 2x + 1 = 23 \\ = > 2x = 23 - 1 \\ = > 2x = 22 \\ = > x = \frac{22}{2} \\ = > x = 11$

Hence required numbers are 11 and (11+1) = 12