# Product

The product of two consecutive odd numbers is 8463. What are this numbers?

Result

x =  91
y =  93

#### Solution:

$xy = 8463 \ \\ y = x+2 \ \\ x>0 \ \\ \ \\ x(x+2)= 8463 \ \\ x^2 +2x - 8463 =0 \ \\ x_{1,2} = \dfrac{ -b \pm \sqrt{ D } }{ 2a } = \dfrac{ -2 \pm \sqrt{ 33856 } }{ 2 } \ \\ x_{1,2} = \dfrac{ -2 \pm 184 }{ 2 } \ \\ x_{1,2} = -1 \pm 92 \ \\ x_{1} = 91 \ \\ x_{2} = -93 ; x>0 \ \\ x = 91$
$y = x+ 2 = 93$

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