document.write( "Question 1150078: Find the difference (x-y) if 4x-3y-sqrt(4x-3y) = 56 and 7x-2y+sqrt(7x-2y) = 12. \n" ); document.write( "

Algebra.Com's Answer #771440 by ikleyn(52800) $\"\"$ $\"About$

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document.write( "(1)  If   4x-3y - sqrt(4x-3y) = 56,  then introduce  t = sqrt(4x-3y) and get the equation\r\n" );
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document.write( "         t^2 - t = 56,  t^2 - t - 56 = 0,  (t-8)*(t+7) = 0.\r\n" );
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document.write( "     The roots are 8 or -7.  In what follows, I will consider only positive value of .\r\n" );
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document.write( "     So,  sqrt(4x-3y) = 8;  hence,  4x - 3y = 64.\r\n" );
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document.write( "(2)  Follow by the same way, and from the second equation,  7x-2y + sqrt(7x-2y) = 12  find\r\n" );
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document.write( "         t = sqrt(7x-2y),  t^2 +t -12 = 0,  (t-3)*(t+4) = 0.\r\n" );
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document.write( "     Of the two roots for sqrt, take only positive  t= 3.\r\n" );
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document.write( "     It gives  sqrt(7x-2y) = 3;  hence  7x - 2y = 9.\r\n" );
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document.write( "(3)  Now you have the system of 2 equations in 2 unknowns\r\n" );
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document.write( "         4x - 3y = 64,\r\n" );
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document.write( "         7x - 2y =  9.\r\n" );
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document.write( "     Solve it by any way and any method you know (it is just arithmetic) and find x and y.\r\n" );
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document.write( "(4)  Then calculate x-y.\r\n" );
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