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If(x ^2+x + 1 ) /(x ^ 2+2x+ 1 )= A +(B)/(x + 1 ) + (C )/((x + 1 ) ^ 2 ), thenA - Bisequalto |
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Answer» Solution :GIVENTHAT, `(X ^ 2+x+ 1 ) /(x ^ 2+2x+ 1 )=A + (B)/(( x + 1 )) +(C )/((x + 1 ) ^ 2 ) ` ` rArr( x ^ 2+ x+ 1 ) /(x^ 2+ 2x+ 1 )= ( A ( x+ 1 ) ^ 2+ B( x + 1 )+ C)/( ( x + 1 ) ^ 2 ) ` ` rArrx ^ 2+ x + 1= (A x ^ 2+x ( 2A + B)+ ( A + B + C))/( ( x + 1 ) ^ 2 ) ` `therefore A = 1, 2A + B = 1, A + B + C = 1` ` rArr2 (1)+ B = 1, 1 +( -1)+ C = 1` ` rArr B =-1 rArrC =1 ` `thereforeA - B = 1-( -1), 2(C )= 2 (1)` `= 2 "" ` ...(1) ` 2C =2 "" `...(2) `therefore` From (1)and (2) A - B = 2C |
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