SOLUTION: The product of two consecutive even integers plus their sum is 98.Find the numbers.

Question 754917: The product of two consecutive even integers plus their sum is 98.Find the numbers.
Found 2 solutions by sachi, Cromlix:
Answer by sachi(548) (Show Source): You can put this solution on YOUR website!
The product of two consecutive even integers plus their sum is 98.Find the numbers.
let the two consecutive even integers are a,a+2
atq
a*(a+2)+a+(a+2)=98
or a^2+2a+2a=2=98
or a^2+4a-96=0
or a^2+12a-8a-96=0
or a(a+12)-8(a+12)=0
or (a+12)(a-8)=0
or a=-12 or 8
so the pairs of onsecutive even integers are -12 & -10 or 8 & 10

Answer by Cromlix(4381) (Show Source): You can put this solution on YOUR website!
The two numbers are x and x + 2
Their product + sum.
x( x + 2) + (x + x + 2)
x^2 + 2x + 2x + 2 = 98
x^2 + 4x + 2 - 98 = 0
(x^2 + 4x - 96)= 0
Factorise: (x - 8)(x + 12) = 0
x = 8 x = -12 (no answer)
One number = 8
Other number = 10
Proof:
Their product + sum = 98
(8 x 10) + (8 + 10) = 98
80 + 18 = 98
Hope this helps
:-)

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