Question

Find the middle term of


${( \frac{a}{x} + \frac{x}{a}) }^{10}$


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Answer 1

${( \frac{a}{x} + \frac{x}{a}) }^{10}$

Here exponent = 10,

So middle term = (10/2) + 1th

= 6th term

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N6th = N5th + 1,

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${( \frac{a}{x} + \frac{x}{a}) }^{10}$

= 10 C 5 $( { \frac{x}{a} })^{10 - 5} \times ({ \frac{a}{x} )}^{5}$

= 10!/5! × $( { \frac{x}{a} })^{5} \times ({ \frac{a}{x} )}^{5}$

= 10!/5! ×

$\frac{ \cancel{x^{5}} }{ \cancel{a ^{5} } } \times \frac{ \cancel{ {a}^{5} }}{ \cancel{ {x}^{5} }} .$

= 10!/5!

= 10*9*8*7*6*5!/5!*5*4*3*2

= 2*9*2*7

= 252.

Answer 2

this is the right answer

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