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Let (x + 10)^(50) + (x - 10)^(50) = a(0...

Let `(x + 10)^(50) + (x - 10)^(50) = a_(0) + a_(1) x + a_(2)X^(2) + ….. + a_(50) x^(50)`, for all `x in R`, then `(a_(2))/(a_(0))` is equal to

A

12.25

B

12.5

C

12

D

12.75

Text Solution

Verified by Experts

The correct Answer is:
A
We have , `(x+10)^(50) +(x-10)^(50)=a_(0)+a_(1)x+a_(2)x^(2)+...+a_(50)x^(50) `
`:. a_(0)+a_(1)x+a_(2)x^(2)+...+a_(50)x^(50)`
`=[""^(50)C_(0)x^(50)+""^(50)C_(1)x^(49)10+""^(50)C_(2)x^(48)*10^(2)+...+""^(50)C_(50)10^(50))+(""^(50)C_(0)x^(50)-""^(50)C_(1)x^(49).10+""^(50)C_(2)x^(48)10^(2)+...+""^(50)C_(50) 10^(50))]`
` =2[""^(50)C_(0)x^(50) +""^(50)C_(2)x^(48)*10^(2)+""^(50)C_(4)x^(46)*10^(4) +...+""^(50)C_(50) *10^(50)]`
By comparing coefficients, we get
`a_(2)=2""^(50)C_(48)(10)^(48),a_(0)=2""^(50)C_(50)(10)^(50)=2(10)^(50)`
`:. (a_(2))/(a_(0))=(2(""^(50)C_(2))(10)^(48))/(2(10)^(50))=2(50*49)/(1*2)((10)^(48))/(2*(10)^(50)) " " [ :' ""^(50)C_(48)=""^(50)C_(2)]`
` =(50xx49)/(2*(10xx10))=(5xx49)/(20)=(245)/( 20)=12.25`
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