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 x2+2x8463=0 x1,2=b±D2a=2±338562 x1,2=2±1842 x1,2=1±92 x1=91 x2=93;x>0 x=91xy = 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=93y = x+ 2 = 93



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