Question

Natural number is greater than the other by 5.the sum of their square is 73.find those numbers

Answer 1

x > 5 + x

x ² + x ² + 2 5 + 1 0 x = 7 3

2 x ² + 1 0 x = 7 3 - 2 5

x ² + x = 4 8 / 20

x ² = 48 / 40

x = sqrt 4 8 / 40

x = 0.1732

Answer 2

Step-by-step explanation:

$\huge\blue{\underline{\underline{\bf Question}}}$

Natural number is greater than the other by 5.the sum of their square is 73.find those numbers

$\huge\blue{\underline{\underline{\bf Answer}}}$

Let x and x +5 be the natural number..

Sum of the squares is 73

$\implies {x}^{2} + {(x + 5)}^{2} = 73 \\ \\ \implies {x}^{2} + {x}^{2} + 25 + 10x = 73 \\ \\ \implies 2 {x}^{2} + 10x + 25 - 73 = 0 \\ \\ \implies 2 {x}^{2} + 10x - 48 = 0 \\ \\ \implies {x}^{2} + 5x - 24 = 0 \\ \\ \implies x = \frac{ - 5 + \: or \: - \sqrt{ {5}^{2} - 4(1)( - 24)} }{2(1)} \\ \\ \implies x = \frac{ - 5 + \: or \: - \sqrt{25 + 96} }{2} \\ \\ \implies x = \frac{ - 5 + \: or \: - \sqrt{121} }{2} \\ \\ \implies x = \frac{ - 5 + \: or \: - 11}{2} \\ \\ \implies \huge \boxed{ \: x = 3 \: \: \: \: or \: \: \: x = - 8}$