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The sum of two positive real numbers is 17 and their product is 40. Find the positive difference of those two numbers. Answer is not 1, or 2√129

User Micky Loo
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The positive difference between these two numbers is ∣8−9∣=1.

Let x and y be the two positive real numbers.

Given:

x+y=17

xy=40

We want to find the positive difference between these two numbers, which is ∣x−y∣.

Let's solve for x and y using these equations:

From x+y=17, we can express y in terms of x as y=17−x.

Substituting this expression for y into the equation xy=40:

x(17−x)=40

17x−x^2 =40

x^2 −17x+40=0

Now, let's factorize or use the quadratic formula to solve for x:

x^2 −17x+40=0

(x−8)(x−9)=0

Setting each factor equal to zero:

x−8=0 or x−9=0

x=8 or x=9

So, the two numbers are x=8 and y=17−x=17−8=9 or x=9 and y=17−x=17−9=8.

Therefore, the positive difference between these two numbers is ∣8−9∣=1.

User Connor Gramazio
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