document.write( "Question 30041: Please help me solve this equation:
\n" ); document.write( "The sum of two numbers is 6 & their product is 4. Find the larger of the two numbers.\r
\n" ); document.write( "\n" ); document.write( "Thanks:) \n" ); document.write( "
Algebra.Com's Answer #16776 by sdmmadam@yahoo.com(530)\"\" \"About 
You can put this solution on YOUR website!
The sum of two numbers is 6 & their product is 4.
\n" ); document.write( "Let the two numbers be A and B say with A > B
\n" ); document.write( "The sum of two numbers is 6
\n" ); document.write( "A+B =6 ----(1)
\n" ); document.write( "their product is 4
\n" ); document.write( "AB = 4 ----(2)
\n" ); document.write( "We have by formula (A-B)^2 = (A+B)^2-4AB
\n" ); document.write( "Therefore (A-B)^2 = 6^2-4X4 = 36-16 = 20
\n" ); document.write( "(A-B)^2 = 20
\n" ); document.write( "Therefore taking the positive sqrt (since A > B, we have (A-B) > 0)
\n" ); document.write( "(A-B) = sqrt(20)
\n" ); document.write( "That is A - B = 2sqrt of 5 ----(3)
\n" ); document.write( "And A+B = 6 ----(1)
\n" ); document.write( "(3)+(1) implies
\n" ); document.write( "(A+A) = 2(rt5)+6
\n" ); document.write( "2A = 2(rt5)+6
\n" ); document.write( "dividing by 2
\n" ); document.write( "Therefore A = [sqrt(5)+3]
\n" ); document.write( "Putting A = [sqrt(5)+3] in (1)
\n" ); document.write( "B = 6-A
\n" ); document.write( "B =6 -[sqrt(5)+3] = 6 - sqrt(5)-3 = (6-3)-sqrt(5) = 3-sqrt(5)
\n" ); document.write( "Answer: A = [3+ sqrt of 5] and B = [3 -sqrt of 5]
\n" ); document.write( "Verification: AB = [3+ sqrt of 5]X[3 -sqrt of 5]
\n" ); document.write( "=3^2- (rt5)^2 = 9-5 = 4 which is correct
\n" ); document.write( " \r
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "
\n" );