SOLUTION: a man is x<2 (X square) years old while his son is x years old. In 4X years time ,the man will be twice as old as his son. Form an equation and solve it to find the value of X.

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons -> SOLUTION: a man is x<2 (X square) years old while his son is x years old. In 4X years time ,the man will be twice as old as his son. Form an equation and solve it to find the value of X.      Log On


   

Question 971204: a man is x<2 (X square) years old while his son is x years old. In 4X years time ,the man will be twice as old as his son. Form an equation and solve it to find the value of X.
Found 2 solutions by josgarithmetic, MathTherapy:
Answer by josgarithmetic(39616) About Me  (Show Source):
You can put this solution on YOUR website!
Please refer now to this request question posting:
http://www.algebra.com/algebra/homework/quadratic/Quadratic_Equations.faq.question.971209.html

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Description is poorly written. m for man s for son;
The inequality shown does not make sense. x%3C2x%5E2, is what?
m%3Cx%3C2x%5E2 and s=x?
This could be m%3C2x%5E2.

Let 4x years pass; then
2%28m%2B4x%29=%28s%2B4x%29

The only understanding is a system
system%28m%3C2x%5E2%2C2%28m%2B4x%29=s%2B4x%29.

2m%2B8x=s%2B4x
2m-s=-8x%2B4x
2m-s=-4x
2m=s-4x
m=%28s-4x%29%2F2

Use m in the inequality.
%28s-4x%29%2F2%3C2x%5E2
s-4x%3C4x%5E2
s-4x-4x%5E2%3C0
-s%2B4x%2B4x%5E2%3E0
4x%5E2%2B4x-s%3E0, a parabola with a minimum for a vertex. The inequality will be true to the left of the lesser root and to the right of the greater root. The polynomial must have two real roots.
Look at the discriminant.
4%5E2-4%2A4%2A%28-s%29%3E0, because the discriminant must be positive.
16%2B16s%3E0
1%2Bs%3E0
1%3E-s
-1%3Cs------------which seems to indicate that the son is ONE YEAR BEFORE BEING BORN.

Write the inequality using this value for s.
highlight_green%284x%5E2%2B4x-%28-1%29%3E0%29
4x%5E2%2B4x%2B1%3E0
Now what are the roots for this polynomial?
x=%28-4%2B-+sqrt%2816-4%2A4%28-1%29%29%29%2F8
x=%28-4%2B-+sqrt%2832%29%29%2F8
x=%28-4%2B-+sqrt%282%5E5%29%29%2F8
x=%28-4%2B-+16sqrt%282%29%29%2F8
x=%28-1%2F2%2B-+2%2Asqrt%282%29%29
We must use the positive, or PLUS form for x.
highlight%28x%3E2sqrt%282%29-1%2F2%29, in order to satisfy the inequality.

Look carefully at the problem description as it is given to you and write the exact problem description, word for word to be sure you did not mis-state it in the help request. What is shown in your request here seems overly complicated but appeared finally solvable.

Answer by MathTherapy(10551) About Me  (Show Source):
You can put this solution on YOUR website!

a man is x<2 (X square) years old while his son is x years old. In 4X years time ,the man will be twice as old as his son. Form an equation and solve it to find the value of X.
highlight_green%28x+=+6%29, with x = X

Why do you have to complicate matters by using x and X? These are different variables, and therefore suggest DIFFERENT values.