document.write( "Question 455232: Twice the sum of two numbers is 28. The sum of the squares of the two numbers is 100. What is the product of the two numbers? \n" ); document.write( "
Algebra.Com's Answer #312569 by mathmartian(7)\"\" \"About 
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Let's begin by using the variables x and y to represent the two numbers.
\n" ); document.write( "Next, let's write two algebraic equations to represent the problem.
\n" ); document.write( "For twice the sum of two numbers is 28, we can write 2(x+y)=28
\n" ); document.write( "For the sum of the squares of the two numbers is 100, we can write x²+y²=100
\n" ); document.write( "The problem wants us to solve for the product of the two numbers, or xy.
\n" ); document.write( "Now notice that the key to solving this problem involves squaring equations. \r
\n" ); document.write( "\n" ); document.write( "To simplify, divide both sides of the first equations by 2, to get x+y=14
\n" ); document.write( "Now square this equation. (x+y)²=14²
\n" ); document.write( "Simplify, and you get x²+2xy+y²=196
\n" ); document.write( "See the link yet?
\n" ); document.write( "Well, let's substitute the equation x²+y²=100 into this equation.
\n" ); document.write( "100+2xy=196
\n" ); document.write( "Now subtract 100 from both sides, 2xy=96
\n" ); document.write( "Lastly, divide both sides by 2, and you get your answer, xy=48
\n" ); document.write( "Great job. Keep it up! \n" ); document.write( "
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