document.write( "Question 201238: The sum of two squares of two numbers is 128, the product of the two numbers is 64. what are the 2 numbers? \n" ); document.write( "
Algebra.Com's Answer #151433 by jim_thompson5910(35256)\"\" \"About 
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\"The sum of the squares of two numbers is 128\" translates to \"x%5E2%2By%5E2=128\"\r
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\n" ); document.write( "\n" ); document.write( "\"The product of the numbers is 64\" translates to \"xy=64\"\r
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\n" ); document.write( "\n" ); document.write( "\"xy=64\" Start with the second equation.\r
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\n" ); document.write( "\n" ); document.write( "\"y=64%2Fx\" Divide both sides by \"x\".\r
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\n" ); document.write( "\n" ); document.write( "\"x%5E2%2By%5E2=128\" Move onto the first equation\r
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\n" ); document.write( "\n" ); document.write( "\"x%5E2%2B%2864%2Fx%29%5E2=128\" Plug in \"y=64%2Fx\"\r
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\n" ); document.write( "\n" ); document.write( "\"x%5E2%2B4096%2Fx%5E2=128\" Square \"64%2Fx\" to get \"4096%2Fx%5E2\"\r
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\n" ); document.write( "\n" ); document.write( "\"x%5E4%2B4096=128x%5E2\" Multiply EVERY term by the LCD \"x%5E2\" to clear out the fractions.\r
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\n" ); document.write( "\n" ); document.write( "\"x%5E4%2B4096-128x%5E2=0\" Subtract \"128x%5E2\" from both sides.\r
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\n" ); document.write( "\n" ); document.write( "\"x%5E4-128x%5E2%2B4096=0\" Rearrange the terms.\r
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\n" ); document.write( "\n" ); document.write( "Let \"z=x%5E2\". So \"z%5E2=x%5E4\"\r
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\n" ); document.write( "\n" ); document.write( "\"z%5E2-128z%2B4096=0\" Replace \"x%5E4\" with \"z%5E2\". Replace \"x%5E2\" with \"z\"\r
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\n" ); document.write( "\n" ); document.write( "Notice that the quadratic \"z%5E2-128z%2B4096\" is in the form of \"Az%5E2%2BBz%2BC\" where \"A=1\", \"B=-128\", and \"C=4096\"\r
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\n" ); document.write( "\n" ); document.write( "Let's use the quadratic formula to solve for \"z\":\r
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\n" ); document.write( "\n" ); document.write( "\"z+=+%28-B+%2B-+sqrt%28+B%5E2-4AC+%29%29%2F%282A%29\" Start with the quadratic formula\r
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\n" ); document.write( "\n" ); document.write( "\"z+=+%28-%28-128%29+%2B-+sqrt%28+%28-128%29%5E2-4%281%29%284096%29+%29%29%2F%282%281%29%29\" Plug in \"A=1\", \"B=-128\", and \"C=4096\"\r
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\n" ); document.write( "\n" ); document.write( "\"z+=+%28128+%2B-+sqrt%28+%28-128%29%5E2-4%281%29%284096%29+%29%29%2F%282%281%29%29\" Negate \"-128\" to get \"128\". \r
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\n" ); document.write( "\n" ); document.write( "\"z+=+%28128+%2B-+sqrt%28+16384-4%281%29%284096%29+%29%29%2F%282%281%29%29\" Square \"-128\" to get \"16384\". \r
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\n" ); document.write( "\n" ); document.write( "\"z+=+%28128+%2B-+sqrt%28+16384-16384+%29%29%2F%282%281%29%29\" Multiply \"4%281%29%284096%29\" to get \"16384\"\r
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\n" ); document.write( "\n" ); document.write( "\"z+=+%28128+%2B-+sqrt%28+0+%29%29%2F%282%281%29%29\" Subtract \"16384\" from \"16384\" to get \"0\"\r
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\n" ); document.write( "\n" ); document.write( "\"z+=+%28128+%2B-+sqrt%28+0+%29%29%2F%282%29\" Multiply \"2\" and \"1\" to get \"2\". \r
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\n" ); document.write( "\n" ); document.write( "\"z+=+%28128+%2B-+0%29%2F%282%29\" Take the square root of \"0\" to get \"0\". \r
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\n" ); document.write( "\n" ); document.write( "\"z+=+%28128+%2B+0%29%2F%282%29\" or \"z+=+%28128+-+0%29%2F%282%29\" Break up the expression. \r
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\n" ); document.write( "\n" ); document.write( "\"z+=+%28128%29%2F%282%29\" or \"z+=++%28128%29%2F%282%29\" Combine like terms. \r
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\n" ); document.write( "\n" ); document.write( "\"z+=+64\" or \"z+=+64\" Simplify. \r
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\n" ); document.write( "\n" ); document.write( "So the only solution (in terms of \"z\") is \"z+=+64\"\r
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\n" ); document.write( "\n" ); document.write( "Now recall that we let \"z=x%5E2\". So this means that \"64=x%5E2\" and that \"x=8\" or \"x=-8\"\r
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\n" ); document.write( "\n" ); document.write( "Now let's find \"y\" when \"x=8\":\r
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\n" ); document.write( "\n" ); document.write( "\"y=64%2Fx\" Go back to the first isolated equation.\r
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\n" ); document.write( "\n" ); document.write( "\"y=64%2F8\" Plug in \"x=8\"\r
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\n" ); document.write( "\n" ); document.write( "\"y=8\" Reduce.\r
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\n" ); document.write( "\n" ); document.write( "So when \"x=8\", \"y=8\" giving the ordered pair (8,8)\r
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\n" ); document.write( "\n" ); document.write( "Now let's find \"y\" when \"x=-8\":\r
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\n" ); document.write( "\n" ); document.write( "\"y=64%2Fx\" Go back to the first isolated equation.\r
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\n" ); document.write( "\n" ); document.write( "\"y=64%2F%28-8%29\" Plug in \"x=-8\"\r
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\n" ); document.write( "\n" ); document.write( "\"y=-8\" Reduce.\r
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\n" ); document.write( "\n" ); document.write( "So when \"x=-8\", \"y=-8\" giving the ordered pair (-8,-8)\r
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\n" ); document.write( "\n" ); document.write( "Answer:\r
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\n" ); document.write( "\n" ); document.write( "So the two ordered pair solutions are (8,8) and (-8,-8)\r
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\n" ); document.write( "\n" ); document.write( "This means that the two numbers are:\r
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\n" ); document.write( "\n" ); document.write( "8 and 8,\r
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\n" ); document.write( "\n" ); document.write( "OR\r
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\n" ); document.write( "\n" ); document.write( "-8 and -8
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