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A root of the equation17x^2 + 17x tan [2...

A root of the equation`17x^2 + 17x tan [2 tan^-1(1/5) - pi/4] - 10 = 0` is (i) `10/17` (ii)`-1` (iii)`-7/17` (iv)`1`

A

`10/17`

B

`-1`

C

`-7/17`

D

1

Text Solution

Verified by Experts

We have
`tan(2tan^(-1)1/5-(pi)/(4))`
`=tan{tan^(-1)(5)/(12)-tan^(-1)1}`
`=tan{tan^(-1)(5/12-1)/(1+5/12)}=-7/17`
So the given equation is
`17x^(2)-7x-10=0 rarr(x-1)(17x+10)=0 rarr x=1,-(10)/(7)`
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