document.write( "Question 683830: one positive number is 4 more than twice another.. if their product is 448 find the numbers \n" ); document.write( "
Algebra.Com's Answer #423763 by Jolliano(16)\"\" \"About 
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Let x be the greater number and y the smaller one.
\n" ); document.write( "From the 1st line,
\n" ); document.write( "x > 2y by 4.
\n" ); document.write( "That gives us the equation
\n" ); document.write( "x = 2y + 4.....(1)
\n" ); document.write( "From the second line,
\n" ); document.write( "x*y = 448
\n" ); document.write( "xy = 448
\n" ); document.write( "Substitute eqn(1) into (2)
\n" ); document.write( "xy = 448
\n" ); document.write( ":-(2y +4)y = 448
\n" ); document.write( "Expanding the bracket,
\n" ); document.write( "2y^2 + 4y = 448
\n" ); document.write( "Solving this equation using completing the square method.
\n" ); document.write( "Divide through by 2,
\n" ); document.write( "y^2 + 2y = 224.
\n" ); document.write( "y^2 + 2y + (1^2) = 224 +(1^2)
\n" ); document.write( "y^2 + 2y + 1 = 224 + 1
\n" ); document.write( "Factorising the L.H.S,
\n" ); document.write( "(y + 1)^2 = 225
\n" ); document.write( "Find the root of both sides,
\n" ); document.write( "(y + 1) = ±√ 225
\n" ); document.write( "y + 1 = ± 15
\n" ); document.write( "Taking positive root,
\n" ); document.write( "y + 1 = 15
\n" ); document.write( "y = 15 - 1
\n" ); document.write( "y =14
\n" ); document.write( "Then
\n" ); document.write( "x = 2y + 4
\n" ); document.write( "x = 2(14) + 4
\n" ); document.write( "x = 28 + 4
\n" ); document.write( "x = 32.
\n" ); document.write( "Taking negative root,
\n" ); document.write( "y + 1 = -15
\n" ); document.write( "y = -15 - 1
\n" ); document.write( "y = -16
\n" ); document.write( "Then
\n" ); document.write( "x = 2y + 4
\n" ); document.write( "x = 2(-16) + 4
\n" ); document.write( "x = -32 + 4
\n" ); document.write( "x = -28 \n" ); document.write( "
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