document.write( "Question 1037851: Find the value of (a+b)/(a-b) if (a+b)^2 = 8ab and a^2 + b^2 = 6ab. a and b are real numbers\r
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Algebra.Com's Answer #652666 by ikleyn(52782)\"\" \"About 
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\n" ); document.write( "Find the value of (a+b)/(a-b) if (a+b)^2 = 8ab and a^2 + b^2 = 6ab. a and b are real numbers
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\n" ); document.write( "\n" ); document.write( "There is much shorter and much straightforward solution.\r
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document.write( "Instead of \"%28a%2Bb%29%2F%28a-b%29\", let us consider the square of this expression,\r\n" );
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document.write( "\"%28a%2Bb%29%5E2%2F%28a-b%29%5E2\".  \r\n" );
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document.write( "It is  \"%28a%2Bb%29%5E2%2F%28a-b%29%5E2\" = \"%288ab%29%2F%28a%5E2-2ab%2Bb%5E2%29\"   ( <--- I replaced \"%28a%2Bb%29%5E2\" in the numerator by  8ab  according to the condition )\r\n" );
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document.write( "= \"%288ab%29%2F%286ab-2ab%29\" =                    ( <--- I replaced \"a%5E2+%2B+b%5E2\" in the denominator by  6ab  according to the condition )\r\n" );
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document.write( "= \"%288ab%29%2F%284ab%29\" = 2.\r\n" );
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document.write( "Since the square of the expression is equal to 2, the expression itself is +/-\"sqrt%282%29\":\r\n" );
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document.write( "\"%28a%2Bb%29%2F%28a-b%29\" = +/-\"sqrt%282%29\".\r\n" );
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