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प्रश्न
Find the constant term (term independent of x) in the expansion of `(sqrt(x) - 3/x^2)^10`
उत्तर
Let tr+1 be the constant term in the expansion of `(sqrt(x) - 3/x^2)^10`.
We know that, in the expansion of (a+ b)n,
tr+1 = nCr an–r br
Here a = `sqrt(x)`, b = `-3/x^2`, n = 10
∴ tr+1 = `""^10"C"_"r" (sqrt(x))^(10-"r") (-(3)/x^2)^"r"`
= `""^10"C"_"r" x^(5-1/2"r")*(-3)^"r"x^(-2"r")`
= `""^10"C"_"r" (-3)^"r"* x^(5 - 5/2"r")`
But tr+1 is a constant term
∴ power of x = 0
∴ `5 - 5/2"r"` = 0
∴ r = 2
∴ the constant term = 10C2 (– 3)2
= `(10 xx 9)/(1 xx 2) xx 9`
= 405
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