SOLUTION: Solve the following problems involving applications of polynomials. Three consecutive even integers are such that the square of the third is 76 more than the square of the secon

Question 143270: Solve the following problems involving applications of polynomials.
Three consecutive even integers are such that the square of the third is 76 more than the square of the second. Find the three integers.

Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
Three consecutive even integers:
x, (x+2), (x+4)
:
are such that the square of the third is 76 more than the square of the second.
(x+4)^2 = (x+2)^2 + 76
FOIL
x^2 + 8x + 16 = x^2 + 4x + 4 + 76
:
Arrange the x's on the left and the numbers on the right:
x^2 - x^2 + 8x - 4x = 4 + 76 - 16
:
4x = 64
x =
x = 16 is the 1st even integers
:
Find the three integers.
16, 18, 20
:
:
Check solution in the statement:
"square of the third is 76 more than the square of the second."
20^2 = 18^2 + 76
400 = 324 + 76; confirms our solution
:
C
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