Question

Write each each of the following number as different of the square two consecutive natural number i) 49 ii) 75

Answer 1

(i)

$(x + 1) {}^{2} - {x}^{2} = 49 \\ {x}^{2} + 2x + 1 - {x}^{2} = 49 \\ 2x + 1 = 49 \\ 2x = 48 \\ x = 48 \div 2 \\ = 24 \\ first \: number \: is \: 24 \: and \: second \: number \: is \: 25$

(ii)

$2x + 1 = 75 \\ 2x = 74 \\ x = 74 \div 2 \\ = 37 \\ first \: numbe \: is \: 37 \: and \: second \: number \: is \: 38$