Answered

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The product of two consecutive positive odd numbers is 575. Find the smaller of the two numbers?

Sagot :

MrRoyal

Answer:

The smaller number is 23

Step-by-step explanation:

Given

Let the odd numbers be x and y [x, being the smallest]

Such that

[tex]y = x + 2[/tex]

and

[tex]x * y = 575[/tex]

Required

Find x

Substitute [tex]y = x + 2[/tex] in [tex]x * y = 575[/tex]

[tex]x * [x + 2] = 575[/tex]

Open bracket

[tex]x^2+ 2x = 575[/tex]

Equate to 0

[tex]x^2+ 2x - 575 =0[/tex]

Expand

[tex]x^2+ 25x -23x- 575 =0[/tex]

Factorize

[tex]x(x+ 25) -23(x+ 25) =0[/tex]

Factor out x + 25

[tex](x-23) (x+ 25) =0[/tex]

Solve

[tex]x - 23 = 0[/tex] or [tex]x - 25 =0[/tex]

[tex]x= 23[/tex] or [tex]x = -25[/tex]

But x can't be negative.

So:

[tex]x= 23[/tex]

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