Question

the sum of positive integers and its square is 90 find the number

Answer 1

x + x^2 = 90; so

x^2 + x -90 = 0

(x +10)(x-9) = 0

x = 9 or -10.

Hope that helps.

Answer 2

Let the positive integer be 'x'

$according \: to \: question \\ \\ x + {x}^{2} = 90 \\ \\ = > {x}^{2} + x - 90 = 0 \\ \\ = > {x}^{2} + 10x - 9x - 90 = 0 \\ \\ = > x(x + 10) - 9(x + 10) = 0 \\ \\ (x - 9)(x + 10) = 0 \\ \\ now \\ x - 9 = 0 \\ = > x = 9 \\ and \\ x + 10 = 0 \\ = > x = - 10$

Since 'x' is an positive integer

So , x=-10 is not acceptable

Thus , required positive integer is 9

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