SOLUTION: 3 consecutive even numbers where the product of the smaller two numbers is 52 less than the square of the largest number.

Question 207613: 3 consecutive even numbers where the product of the smaller two numbers is 52 less than the square of the largest number.
Found 2 solutions by checkley77, MathTherapy:
Answer by checkley77(12844) (Show Source): You can put this solution on YOUR website!
Let x, x+1 & x+2 be the three numbers.
x(x+1)+52=(x+2)^2
x^2+x+52=x^2+4x+4
x^2-x^2-4x+x=4-52
-3x=-48
x=-48/-3
x=16 ans. for the smallest number
16=1=17 ans. for the middle number
16+2=18 ans. for the largest number
Proof
16*17+52=18^2
272+52=324
324=324

Answer by MathTherapy(10552) (Show Source): You can put this solution on YOUR website!

3 consecutive even numbers where the product of the smaller two numbers is 52 less than the square of the largest number.

Let the smallest number be S

Then the other two numbers, since these are EVEN numbers are: S + 2, and S + 4

Now, since the product of the smaller two numbers is 52 less than the square of the largest number, we have:

2S - 8S = 16 - 52
- 6S = - 36
= 6

Therefore, the smallest number is , the second smallest is (6 + 2), and the largest is (6 + 4)

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Check:
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The product of the two smaller numbers, 6 and 8 is 48 (6 * 8)

The square of the largest number, 10, is 100 ()

48 (the product of the two smaller numbers) is 52 less than 100 (the square of the largest number)

PLUS, the THREE are CONSECUTIVE EVEN NUMBERS

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