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Algebra.Com's Answer #10490 by venugopalramana(3286)![\"\"](\"/images/stars/stars-13.gif\")  You can put this solution on YOUR website! \r \n" ); document.write( "\n" ); document.write( " \n" ); document.write( "this prolem has no solution..reason is as follows ...we have square root of (t-2) on the r.h.s.for it to be real or meaning full,t should be equal to 2 or more than 2,since then only t-2 can have a square root.but if t>=2,then on the l.h.s.we have 2t+3 which will be definitely more than t-2,on the r.h.s.so \n" ); document.write( "sqrt.of (2t+3)on l.h.s.will be more than sq.rt.of (t-2) on the r.h.s.then obviously we cant get the r.h.s. by adding 2 to the l.h.s. \n" ); document.write( "IF YOU ARE DOING COMPLEX NUMBERS PLEASE TELL ME...TO GIVE YOU THE METHOD OF ATTACK FOR THAT \n" ); document.write( "OR LET ME MODIFY THE PROBLEM TO GIVE YOU THE METHOD OF SOLUTION \n" ); document.write( " \n" ); document.write( " \n" ); document.write( "square both sides,we get \n" ); document.write( "2t+3+t-2+2*sq.rt.{(2t+3)*(t-2)}=4 \n" ); document.write( "3t+1-4=2sq.rt(2t^2-4t+3t-6) \n" ); document.write( "3t-3=2sq.rt(2t^2-t-6).....square both sides again \n" ); document.write( "(3t-3)^2=4*(2t^2-t-6) \n" ); document.write( "9t^2+9-2*3*3*t=8t^2-4t-24 \n" ); document.write( "9t^2+9-18t-8t^2+4t+24=0 \n" ); document.write( "t^2-14t+33=0 \n" ); document.write( "t^2-11t-3t+33=0 \n" ); document.write( "t(t-11)-3(t-11)=0 \n" ); document.write( "(t-3)(t-11)=0 \n" ); document.write( "hence t=3 or 11....since we squared the given eqn.twice it is a good practice to back check the answers to ensure that we have not introduced any additional roots by squaring. \n" ); document.write( "so putting t=3 in original eqn. we get \n" ); document.write( " \n" ); document.write( "so putting t=11 in original eqn. we get \n" ); document.write( " |