If , then
(A)
(B)
(C)
(D)

contexto.140

3 years ago

CORRECT OPTION : C

$\begin{array}{l} \tan ^{-1} 2 x+\tan ^{-1} 3 x=\frac{\pi}{4} \\ \tan ^{-1}\left(\frac{2 x+3 x}{1-6 x^{2}}\right)=\frac{\pi}{4} ; x>0 \\ \frac{5 x}{1-6 x^{2}}=1 \\ 5 x=1-6 x^{2} \\ 6 x^{2}+5 x-1=0 \\ 6 x^{2}+6 x-x-1=0 \\ 6 x(x+1)-1(x+1)=0 \\ (6 x-1)(x+1)=0 \\ x \neq-1 ; x=\frac{1}{6} \end{array}$