SOLUTION: the ages of three children in a family can be expressed as consecutive integers. the square of the age of the youngest child is 4 more than 8 times the age of the oldest. find the

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Question 504150: the ages of three children in a family can be expressed as consecutive integers. the square of the age of the youngest child is 4 more than 8 times the age of the oldest. find the ages of the three children
Answer by Maths68(1474) About Me  (Show Source):
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Let
Present age of youngest = x
Present age of older = x+1
Present age of older = x+2
x^2=8(x+2)+4
x^2=8x+16+4
x^2-8x=20
x^2-8x-20=0
x^2-10x+2x-20=0
x(x-10)+2(x-10)=0
(x-10)(x+2)=0
x-10=0 or x+2=0
x=10 or x=-2 (Impossible)
So x=10
Present age of youngest = x = 10
Present age of older = x+1 = 10+1 = 11
Present age of older = x+2 = 10+2 = 12