Question

The difference between the squares of two consecutive whole numbers is 31. find the numbers.​

Answer 1

$\huge\mathfrak{Answer:}$

Let the 2 consecutive whole numbers be x and x+1

According to question

${(x + 1)}^{2} - {x}^{2} = 31 \\ {x }^{2} + 1 + 2x - {x}^{2} = 31 \\ 2x + 1 = 31 \\ 2x = 31 - 1 \\ 2x = 30 \\ x = \frac{30}{2 } \\ x = 15 \\ x + 1 =15 + 1 = 16$

Consecutive Numbers are 15 and 16

Answer 2

SOLUTION:-

Let the first number= x &

the second number= x+1

According to the question,

$( {x + 1)}^{2} - ( {x)}^{2} = 31 \\ \\ = > {x}^{2} + 2x + 1 - {x}^{2} = 31 \\ \\ = > 2x + 1 = 31 \\ \\ = > 2x = 31 - 1 \\ \\ = > 2x = 30 \\ \\ = > x = \frac{30}{2} \\ \\ = > x = 15$

So,

1st number = 15

2nd number= 15+ 1= 16

Hence, the number are 15 & 16.

Hope it helps ☺️