F4 Math一問

let the first consecutive no. be x, the 2nd consecutive no. be (x+2)

x (x+2) = 575
x (2次) +2x = 575
x (2次) +2x -575 = 0
(x+25) (x-23) = 0
x= -25 (reject) or x=23

Therefore, x =23
(x+2)=23+2=25

The 2 consecutive no. are 23 & 25

Your question is : Find two consecutive positive odd integers such that their product is 575.

Solution :
Let x be the smaller positive odd integer, then x+2 will be the larger one(since they are consecutvie and odd, so they are differ by 2)
x(x+2) = 575
x^2 + 2x - 575 = 0
(x-23)(x+25)=0
x=23 or x=-25(rejected since it must be positive)
Therefore the two positive odd integers are 23 and 25.

Let the first positive odd number be x
the consecutive number would be x+2
so their product is
x(x+2) = 575
x^2 + 2x - 575 = 0
(x - 23)(x+25) = 0
x = 23 or -25(rejected)
so the two consecutive positive odd number are 23 and 25

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