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$A$ root of the equation $17 x^{2} + 17 x \tan (2 \tan^{- 1} \frac{1}{5} - \frac{π}{4}) - 10 = 0$ , is

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Correct option is D

We have,tan⁡2tan−1⁡15−π4=tan⁡tan−1⁡512−tan−1⁡1∵2tan−1⁡x=tan−1⁡2x1−x2=tan⁡tan−1⁡512−11+512=−717So, the given equation is17x2−7x−10=0⇒(x−1)(17x+10)=0⇒x=1,−107

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A root of the equation 17x2+17xtan⁡2tan−1⁡15−π4−10=0, is

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$A$ root of the equation $17 x^{2} + 17 x \tan (2 \tan^{- 1} \frac{1}{5} - \frac{π}{4}) - 10 = 0$ , is