document.write( "Question 926468: In the expansion of (x+y)n, the second term is 1620.the third term is 4320 and the fourth term is 5760,find the values of x,y and n \n" ); document.write( "
Algebra.Com's Answer #562363 by Edwin McCravy(20056)\"\" \"About 
You can put this solution on YOUR website!
\r\n" );
document.write( "If you count the terms starting with 0 instead of 1, \r\n" );
document.write( "there are n terms, and the kth term is \"C%28n%2Ck%29x%5Er%2Ay%5E%28n-r%29\"\r\n" );
document.write( "\r\n" );
document.write( "In the expansion of (x+y)n, the second term is 1620.\r\n" );
document.write( "\r\n" );
document.write( "That's the first term if you start counting with 0,  So\r\n" );
document.write( "\r\n" );
document.write( "\"C%28n%2C1%29x%5En%2Ay%5E%28n-1%29=1620\"\r\n" );
document.write( "\r\n" );
document.write( "\"n%2Ax%5En%2Ay=1620\"\r\n" );
document.write( "\r\n" );
document.write( "the third term is 4320\r\n" );
document.write( "\r\n" );
document.write( "That's the second term if you start counting with 0,  So\r\n" );
document.write( "\r\n" );
document.write( "\"C%28n%2C2%29x%5E%28n-2%29%2Ay%5E2=4320\"\r\n" );
document.write( "\r\n" );
document.write( "\"expr%28n%28n-1%29%2F2%29x%5E%28n-2%29%2Ay%5E2=4320\" \r\n" );
document.write( "\r\n" );
document.write( "\"n%28n-1%29x%5E%28n-2%29%2Ay%5E2=8640\" \r\n" );
document.write( "\r\n" );
document.write( "and the fourth term is 5760,\r\n" );
document.write( "\r\n" );
document.write( "That's the third term if you start counting with 0,  So\r\n" );
document.write( "\r\n" );
document.write( "\"C%28n%2C3%29x%5E%28n-3%29%2Ay%5E3=5760\"\r\n" );
document.write( "\r\n" );
document.write( "\"expr%28n%28n-1%29%28n-2%29%2F6%29x%5E%28n-3%29%2Ay%5E3=5760\"\r\n" );
document.write( "\r\n" );
document.write( "\"n%28n-1%29%28n-2%29x%5E%28n-3%29%2Ay%5E3=34560\"\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Divide equal by equals. That is,\r\n" );
document.write( "\r\n" );
document.write( "Divide the sides of the 2nd equation by the sides of the 1st equation\r\n" );
document.write( "\r\n" );
document.write( "\"%28n%28n-1%29x%5E%28n-2%29y%5E2%29%2F%28n%2Ax%5E%28n-1%29%2Ay%29+=8640%2F1620\"\r\n" );
document.write( "\r\n" );
document.write( "Simplify by canceling and subtracting exponents:\r\n" );
document.write( "\r\n" );
document.write( "\"%28%28n-1%29y%29%2Fx=16%2F3\"\r\n" );
document.write( "\"3%28n-1%29y=16x\"\r\n" );
document.write( "\"3%28n-1%29%2F16=x%2Fy\"\r\n" );
document.write( "\r\n" );
document.write( "Divide the sides of the 3rd equation by the sides of the 2nd equation\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Simplify by canceling and subtracting exponents:\r\n" );
document.write( "\r\n" );
document.write( "\"%28%28n-2%29y%29%2Fx=4\"\r\n" );
document.write( "\"%28n-2%29y=4x\"\r\n" );
document.write( "\"%28n-2%29%2F4=x%2Fy\"\r\n" );
document.write( "\r\n" );
document.write( "Setting the expressions for \"x%2Fy\" equal\r\n" );
document.write( "\r\n" );
document.write( "\"3%28n-1%29%2F16=%28n-2%29%2F4\"\r\n" );
document.write( "\r\n" );
document.write( "multiply through by 16\r\n" );
document.write( "\r\n" );
document.write( "\"3%28n-1%29=4%28n-2%29\"\r\n" );
document.write( "\r\n" );
document.write( "\"3n-3=4n-8\"\r\n" );
document.write( "\r\n" );
document.write( "\"5=n\"\r\n" );
document.write( "\r\n" );
document.write( "Taking the first two equations of the system:\r\n" );
document.write( "\r\n" );
document.write( "\"system%28n%2Ax%5E%28n-1%29%2Ay=1620%2Cn%28n-1%29x%5E%28n-2%29y%5E2=8640%29\"\r\n" );
document.write( "\"system%285%2Ax%5E%285-1%29%2Ay=1620%2C5%285-1%29x%5E%285-2%29y%5E2=8640%29\"\r\n" );
document.write( "\"system%285x%5E4%2Ay=1620%2C5%284%29x%5E3y%5E2=8640%29\"\r\n" );
document.write( "\"system%285x%5E4%2Ay=1620%2C20x%5E3y%5E2=8640%29\"\r\n" );
document.write( "\"system%28x%5E4%2Ay=324%2Cx%5E3y%5E2=432%29\"\r\n" );
document.write( "\r\n" );
document.write( "Solve the 1st equation for y\r\n" );
document.write( "\r\n" );
document.write( "\"y=324%2Fx%5E4\"\r\n" );
document.write( "Substitute in the 2nd\r\n" );
document.write( "\"x%5E3%28324%2Fx%5E4%29%5E2=432\"\r\n" );
document.write( "\"x%5E3%28104976%2Fx%5E8%29=432\"\r\n" );
document.write( "\"104976%2Fx%5E5=432\"\r\n" );
document.write( "\"104976%2Fx%5E5=432\"\r\n" );
document.write( "\"104976=432x%5E5\"\r\n" );
document.write( "\"243=x%5E5\"\r\n" );
document.write( "\"root%285%2C243%29=x\"\r\n" );
document.write( "\"3=x\"\r\n" );
document.write( "Substitute in\r\n" );
document.write( "\"y=324%2Fx%5E4\"\r\n" );
document.write( "\"y=324%2F3%5E4\"\r\n" );
document.write( "\"y=324%2F81\"\r\n" );
document.write( "\"y=4\"\r\n" );
document.write( "\r\n" );
document.write( "So x=3, y=4, n=5 \r\n" );
document.write( "\r\n" );
document.write( "Edwin
\n" ); document.write( "
\n" );