document.write( "Question 622156: $\"a=1%2B2x%2B4x%5E2%2B..............\"$ , where -1<2x<1, $\"b=+1%2B3y%2B9y%5E2%2B.............\"$ , where -1<3y<1 and 3y+2x=1, prove that ab=a+b \n" ); document.write( "

Algebra.Com's Answer #391200 by Edwin McCravy(20055) $\"\"$ $\"About$

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document.write( "a =  = \r\n" );
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document.write( "That's an infinite geometric series with first term t₁ = 1,\r\n" );
document.write( "and r = 2x.  And since -1 < 2x < 1 it converges and we can use the formula:\r\n" );
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document.write( " =  = \r\n" );
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document.write( "b =  = \r\n" );
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document.write( "That's also an infinite geometric series with first term t₁ = 3y,\r\n" );
document.write( "and r = 3y.  And since -1 < 3y < 1 we can use the formula:\r\n" );
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document.write( " =  =  \r\n" );
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document.write( "So \r\n" );
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document.write( "a = , b = \r\n" );
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document.write( "ab =  · = \r\n" );
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document.write( "a + b = +{1/(1-3y)}}} =  =\r\n" );
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document.write( " =  =\r\n" );
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document.write( "and we are given that 3y+2x=1, so we replace(3y+2x) by 1\r\n" );
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document.write( " = \r\n" );
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document.write( "So ab and a + b  both equal to \r\n" );
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document.write( "Edwin

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