Question 152194: The sum of the number and its square is twelve times the next higher number. Find the no. Found 2 solutions by edjones, orca:Answer by edjones(8007) (Show Source):
You can put this solution on YOUR website! Let the number = x
x+x^2=12(x+1)
x+x^2=12x+12
x^2-11x-12=0
(x-12)(x+1)=0
x=12 or x=-1
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Check:
12+144=12*13 True
-1+(-1)^2=12*0 True
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Ed
You can put this solution on YOUR website! Let the number be n, then the next higher number is n + 1
The sum of the number and its square can be written as n + n^2.
Twelve times the next higher number can be expressed as 12(n + 1).
As the sum of the number and its square is twelve times the next higher number, we have:
n + n^2 = 12(n + 1)
Solving the quadratic equation for x, we have
n + n^2 = 12n + 12
n^2 - 11n - 12 = 0
(n - 12)(n + 1) = 0
So n = 12 or n = -1
Therefore the number is 12 or -1.
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