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Ifabne0andthe sum ofcoefficientsofx ^ 7 andx ^ 4inthe expansionof((x ^ 2 ) /(a)-(b)/(x) ) ^ (11)is0 , then |
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Answer» `a=B ` `therefore T _(r + 1 )=""^(11)c_r ((X^ 2 )/(a)) ^(11 -r )(( - b ) /( x ) ) ^r` `=""^(11) c _r ((1 )/(a)) ^( 11 - r)( - b) ^rx ^( 22 - 2 r) .x^( - r) ` `=""^(11)c _ r((1 ) /(a)) ^(11 - r )( - b ) ^rx ^(22 -3r ) ` if `x ^(22 - 3r)=x ^7` `rArr22 - 3r=7` `rArr3r=15` `thereforer=5` If`x^( 22-3r )=x ^ 4` `rArr22 -3r= 4 ` `3r =18 ` `r=6 ` `therefore`co -efficientof` T_ 6`+ Co-efficientof`T _ 7=0 ` `rArr""^(11)c _ 6 (( 1 ) /(a)) ^ 5(- b ) ^( 6)+""^(11)c _ 5 (( 1 ) /(a)) ^6(- b ) ^( 5)=0 ` `rArr ""^(11)c _5[ (b^6 )/(a ^5 )-(b^5 ) /(a^6 ) ] =0""[ because""^(11)c _ 5 =""^(11)c _6] ` `rArr(b ^ 6 ) /( a ^5 )=(b ^ 5 ) /(a ^6 ) ` ` rArr(ab) ^6 =(ab) ^ 5 ` ` rArr(ab) ^5 [ab -1 ] =0 ` ` rArrab - 1=0[becauseab ne 0] ` `ab = 1` |
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