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4-2.Quadratic Equations and Inequations
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અસમતા $\sqrt {{{\log }_3}(x) - 1} + \frac{{\frac{1}{2}{{\log }_3}\,{x^3}}}{{{{\log }_3}\,\frac{1}{3}}} + 2 > 0$ ના કેટલા પૂર્ણાક ઉકેલો મળે ?
A
$5$
B
$6$
C
$7$
D
$8$
Solution
$\Rightarrow \log _{3} x=t^{2}+1$
$\therefore 2|t|-3\left(1+t^{2}\right)+4>0$
$\therefore 3 t^{2}-3|t|+|t|-1<0$
$\Rightarrow|\mathrm{t}| \in\left(-\frac{1}{3}, 1\right) \Rightarrow \mathrm{t}^{2} \in[0,1)$
$\Rightarrow x \in[3,9) \Rightarrow 6$ integers
Standard 11
Mathematics
