document.write( "Question 1118066: Find the value of A and B if
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Algebra.Com's Answer #733296 by ikleyn(52781)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "Let x be the value (now unknown) exactly half-way between  \"sqrt%28A%29\"  and  \"sqrt%28B%29\",  i.e.  x = \"%28sqrt%28A%29+%2B+sqrt%28B%29%29%2F2\".\r\n" );
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document.write( "So then  \"sqrt%28A%29\" = x + \"sqrt%288%29%2F2\" = x + \"sqrt%282%29\",  \"sqrt%28B%29\" = x - \"sqrt%288%29%2F2\" = \"x+-+sqrt%282%29\".\r\n" );
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document.write( "Then from  \"sqrt%28A%29%2Asqrt%28B%29\" = 4  you get\r\n" );
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document.write( "\"%28x%2Bsqrt%282%29%29%2A%28x-sqrt%282%29%29\" = 4,   or\r\n" );
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document.write( "\"x%5E2+-+%28sqrt%282%29%29%5E2\" = 4,   which is the same as\r\n" );
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document.write( "\"x%5E2+-+2\" = 4,   which implies  \"x%5E2\" = 4 + 2 = 6;  hence,  x = \"sqrt%286%29\".\r\n" );
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document.write( "Then  \"sqrt%28A%29\" = \"sqrt%286%29+%2B+sqrt%282%29\"  ====>  square both sides  ====>  A = \"8+%2B+2%2Asqrt%2812%29\" = \"8+%2B+4%2Asqrt%283%29\".\r\n" );
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document.write( "      \"sqrt%28B%29\" = \"sqrt%286%29+-+sqrt%282%29\"  ====>  square both sides  ====>  B =  \"8+-+2%2Asqrt%2812%29\" = \"8-4%2Asqrt%283%29\".\r\n" );
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