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Find the middle term expansion (x/y-y/x)^10 |
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Answer» Answer: Answer ( y
− x y
)
∵n=7(odd) There will be two middle TERMS, i.e., ( 2 n+1
) th term and ( 2 n+3
) th term. ∵n=7 Middle term in the expansion ( y x
− x y
) 7 will be 4 th and 5 th terms. As we know that general term of the expansion (a+B) n will be- T r+1
= n
C r
a n−r b r
Therefore, 4 th term in the expansion ( y x
− x y
) 7 - T 3+1
= 7
C 3
( y x
) 4 ( x y
) 3 = 7
C 3
( y 4
x 4
)( x 3
y 3
)= 7
C 3
y x
5 th term in the expansion ( y x
− x y
) 7 - T 4+1
= 7
C 4
( y x
) 3 ( x y
) 4 = 7
C 4
( y 3
x 3
)( x 4
y 4
)= 7
C 4
x y
HENCE the middle term of the expansion ( y x
− x y
) 7 are- T 4
= 7
C 3
y x
and T 5
= 7
C 4
x y
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