document.write( "Question 34722This question is from textbook
\n" ); document.write( ": Prove with a simple equation that the product of four consecutive integers can never be a perfrct square. \n" ); document.write( "

Algebra.Com's Answer #20983 by venugopalramana(3286) $\"\"$ $\"About$

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LET THE 4 CONSECUTIVE INTEGERS BE N-1,N,N+1,N+2
\n" ); document.write( "THEIR PRODUCT = P =(N-1)N(N+1)(N+2)=(N^2-1)(N^2+2N)=N^4+2N^3-N^2-2N....IF THIS IS TO BE A PERFECT SQUARE THEN IT SHOULD BE IN THE FORM OF
\n" ); document.write( "(N^2+AN)^2...SINCE THERE IS NO CONSTANT TERM IN P...EXPANDING
\n" ); document.write( "(N^2+AN)^2=N^4+2AN^3+A^2N^2..EQUATING WITH P WE SHOULD HAVE
\n" ); document.write( "2A=1...OR...A=1/2
\n" ); document.write( "A^2=-1..AND -2N=0.....WHICH IS NOT POSSIBLE .....HENCE P CANNOT BE WRITTEN AS A PERFECT SQUARE. \n" ); document.write( "

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