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Question Number 138999 by bramlexs22 last updated on 21/Apr/21

$$\mathrm{The}\mathrm{number}\mathrm{of}\mathrm{solutions}$$$$\mathrm{of}\mathrm{equations}\sqrt{13-18\tan \mathrm{x}}=6\tan \mathrm{x}-3$$$$\mathrm{where}-2\pi <\mathrm{x}<2\pi \mathrm{is}$$

Answered by EDWIN88 last updated on 21/Apr/21

$$\left(1\right)13-18\tan \mathrm{x}⩾0;\tan \mathrm{x}⩽\frac{13}{18}$$$$\left(2\right)13-18\tan \mathrm{x}=36\tan {}^2\mathrm{x}-36\tan \mathrm{x}+9$$$$36\tan {}^2\mathrm{x}-18\tan \mathrm{x}-4=0$$$$18\tan {}^2\mathrm{x}-9\tan \mathrm{x}-2=0$$$$\tan \mathrm{x}=\frac{9\pm 15}{36}=\{\begin{array}{l}\tan \mathrm{x}=\frac{2}{3}\\ \tan \mathrm{x}=-\frac{1}{6}\end{array}$$

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