Question

Find two numbers such that their sum is 12 and their product is 23

Answer 1

Step-by-step explanation:

Let the numbers be x and y

$x + y = 12 \\ x.y = 23 \\ {(x + y)}^{2} = {12}^{2} \\ { x}^{2} + {y}^{2} + 2xy = 144 \\ {x}^{2} + {y}^{2} + 2(23) = 144 \\ {x}^{2} + {y}^{2} = 98 \\ {(x - y)}^{2} = {x}^{2} + {y}^{2} - 2xy \\ {(x - y)}^{2} = 98 - 46 = 52 \\ x - y = \sqrt{52} \\ solving \: both \: eqns \\ x = 6 + \sqrt{13} \\ y = 6 - \sqrt{13 }$

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