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If tan^(-1)(x+3/x)-tan^(-1)(x-3/x)=tan^(...

If `tan^(-1)(x+3/x)-tan^(-1)(x-3/x)=tan^(-1)6/x ,` then the value of `x^4` is_____.

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The correct Answer is:
9
`tan^(-1) (x + (3)/(x)) - tan^(-1) (x -(3)/(x)) = tan^(-1).(6)/(x)`
or `tan^(-1) (((x + (3)/(x)) - (x -(3)/(x)))/(1 + (x + (3)/(x)) (x -(3)/(x)))) = tan^(-1).(6)/(x)`
`rArr x^(2) -(9)/(x^(2)) = 0 " or " x^(4) = 9`
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