Question

find the constant term(term independent of x) in the expansion of (√x-3/x^2)^10
$( \sqrt{x} - 3 \div {x}^{2} ) ^{10}$
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Answer 1

Step-by-step explanation:

Given, expression

$( \sqrt{x} - \frac{3}{ {x}^{2} } )^{10}$

Let the r th term be the term independent of x

so,

$t _{r + 1} = \: ^{10}c_{r} ({ \sqrt{x} })^{10 - r} .( \frac{3}{ {x}^{2} } )^{r}$

$t _{r + 1} = \: ^{10}c_{r} (x)^ \frac {10 - r}{2} . {3}^{r} . {x}^{ - 2r}$

$t _{r + 1} = \: ^{10}c_{r}. {3}^{r} . {x}^{ \frac{10 - r}{ 2} - 2r}$

$t _{r + 1} = \: ^{10}c_{r}. {3}^{r} . {x}^{ \frac{10 -5 r}{ 2} }$

To be independent of x, the power of x should be 0

so,

$\frac{10 - 5r}{2} = 0$

$\implies \: r = 2$