Question

Express the following as the sum of two consecutive integers

1.${21}^2$

2.${13}^2$

3.${11}^2$

4.${19}^2$

Answer 1

In all the cases ,

let one integer be x

since the integers are consecutive,

other integer = x + 1

Now,

a) (x) + (x + 1) = 21²

2x + 1 = 441

2x = 440

x = 440/2 = 220. and x+1 = 221

So,

the integers are 220 and 221

b) 13²

x + x + 1 = 13²

2x + 1 = 169

2x = 168

x = 168/2 = 84. and x + 1 = 85

So,

the consecutive integers are 84 and 85

c) 11²

x + x + 1 = 11²

2x + 1 = 121

2x = 120

x = 120/2

x = 60. and x + 1 = 61

So,

the consecutive integers are 60 and 61

d) 19²

x + x + 1 = 19²

2x + 1 = 361

2x = 360

x = 360/2

x = 180. and x + 1 = 181

So,

the consecutive integers are 180 and 181