Answer:.
Step-by-step explanation:
Answer:
The first set of consecutive even integers equals (8 , 6)
The second set is ( - 8 and - 6) which also works.
Step-by-step explanation:
Equation
(x)^2 + (x + 2)^2 = (x)(x + 2) + 52 Remove the brackets on both sides
Solution
x^2 + x^2 + 4x + 4 = x^2 + 2x + 52 Collect the like terms on the left
2x^2+ 4x+ 4 = x^2 + 2x + 52 Subtract right side from left
2x^2 - x^2 + 4x - 2x + 4 - 52 = 0 Collect the like terms
x^2 + 2x - 48 = 0 Factor
(x + 8)(x - 6) = 0
Answer
Try the one you know works.
x - 6 = 0
x = 6
Therefore the two integers are 6 and 8
6^2 + 8^2 = 100
6*8 + 52 = 100
So 6 and 8 is one set of consecutive even numbers that works.
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What about the other set.
x + 8 = 0
x = - 8
x and x + 2
- 8 and -8 + 2 = - 8, - 6
(- 8 )^2 + (- 6)^2 = 100
(-8)(-6) + 52 = 100
Both sets of consecutive numbers work.
I can't solve it but you can enter the equation into www.quickmath.com and it will give you the answer. Hope it helps.
I believe the answer would be (-3,-5).
Place the equations on top of each other and figure out how to cancel out one of the digits to get your answer. Try canceling out 2x. Multiply the entire equation y=x+3 by -2 to contradict the second equation. y=x(-2)+3(-2) then you'd get y=-2x-6. -2x-6 above 2x+1, solve. -2 and 2 cancel out so you're left with -6+1, therefore, y=5. Now that you have your y, you must solve for x. Using substitution to solve the equation (I picked 2x+1) you'd get -5=2x+1. Subtract 1 on both sides. +1-1=0 so that cancels out. -5-1=-6 and you're left with -6=2x. So you subtract 2 on both sides because 2 has the variable, and you are left with x=-3. Therefore, the answer is (-3,-5).
