Question

the sum of number and its square is 72 find the number

word problem

Answer 1

Hello,

Solution: let the number is x and it's square is
${x}^{2}$
A.T.Q
$x + {x}^{2} = 72 \\ \\ {x}^{2} + x - 72 = 0 \\ \\ {x}^{2} + 9x - 8x - 72 = 0 \\ \\ x(x + 9) - 8(x + 9) = 0 \\ \\ (x + 9)(x - 8) = 0 \\ \\ x = 8 \\ \\ x = - 9$
The number can be 8 and -9.
Both satisfying the equation.


$8 + {8}^{2} = 72$
$- 9 + ( { - 9)}^{2} = - 9 + 81 = 72$

hope it helps you