document.write( "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. \n" ); document.write( "

Algebra.Com's Answer #593758 by josgarithmetic(39617) $\"\"$ $\"About$

You can put this solution on YOUR website!
Please refer now to this request question posting:
\n" ); document.write( "http://www.algebra.com/algebra/homework/quadratic/Quadratic_Equations.faq.question.971209.html\r
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\n" ); document.write( "Description is poorly written. m for man s for son;
\n" ); document.write( "The inequality shown does not make sense. $\"x%3C2x%5E2\"$ , is what?
\n" ); document.write( " $\"m%3Cx%3C2x%5E2\"$ and $\"s=x\"$ ?
\n" ); document.write( "This could be $\"m%3C2x%5E2\"$ .\r
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\n" ); document.write( "\n" ); document.write( "Let 4x years pass; then
\n" ); document.write( " $\"2%28m%2B4x%29=%28s%2B4x%29\"$ \r
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\n" ); document.write( "\n" ); document.write( "The only understanding is a system
\n" ); document.write( " $\"system%28m%3C2x%5E2%2C2%28m%2B4x%29=s%2B4x%29\"$ .\r
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\n" ); document.write( "\n" ); document.write( " $\"2m%2B8x=s%2B4x\"$
\n" ); document.write( " $\"2m-s=-8x%2B4x\"$
\n" ); document.write( " $\"2m-s=-4x\"$
\n" ); document.write( " $\"2m=s-4x\"$
\n" ); document.write( " $\"m=%28s-4x%29%2F2\"$ \r
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\n" ); document.write( "\n" ); document.write( "Use m in the inequality.
\n" ); document.write( " $\"%28s-4x%29%2F2%3C2x%5E2\"$
\n" ); document.write( " $\"s-4x%3C4x%5E2\"$
\n" ); document.write( " $\"s-4x-4x%5E2%3C0\"$
\n" ); document.write( " $\"-s%2B4x%2B4x%5E2%3E0\"$
\n" ); document.write( " $\"4x%5E2%2B4x-s%3E0\"$ , 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.\r
\n" ); document.write( "\n" ); document.write( "Look at the discriminant.
\n" ); document.write( " $\"4%5E2-4%2A4%2A%28-s%29%3E0\"$ , because the discriminant must be positive.
\n" ); document.write( " $\"16%2B16s%3E0\"$
\n" ); document.write( " $\"1%2Bs%3E0\"$
\n" ); document.write( " $\"1%3E-s\"$
\n" ); document.write( " $\"-1%3Cs\"$ ------------which seems to indicate that the son is ONE YEAR BEFORE BEING BORN.\r
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\n" ); document.write( "\n" ); document.write( "Write the inequality using this value for s.
\n" ); document.write( " $\"highlight_green%284x%5E2%2B4x-%28-1%29%3E0%29\"$
\n" ); document.write( " $\"4x%5E2%2B4x%2B1%3E0\"$
\n" ); document.write( "Now what are the roots for this polynomial?
\n" ); document.write( " $\"x=%28-4%2B-+sqrt%2816-4%2A4%28-1%29%29%29%2F8\"$
\n" ); document.write( " $\"x=%28-4%2B-+sqrt%2832%29%29%2F8\"$
\n" ); document.write( " $\"x=%28-4%2B-+sqrt%282%5E5%29%29%2F8\"$
\n" ); document.write( " $\"x=%28-4%2B-+16sqrt%282%29%29%2F8\"$
\n" ); document.write( " $\"x=%28-1%2F2%2B-+2%2Asqrt%282%29%29\"$
\n" ); document.write( "We must use the positive, or PLUS form for x.
\n" ); document.write( " $\"highlight%28x%3E2sqrt%282%29-1%2F2%29\"$ , in order to satisfy the inequality.\r
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\n" ); document.write( "\n" ); document.write( "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. \n" ); document.write( "

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