Question

1 /x2>3 then x=......

Answer 1

Solution :-

Given :-

$\bullet\dfrac{1}{x^2} > 3$

By solving inequality

$\implies \dfrac{1}{x^2} - 3 > 0$

$\implies \dfrac{1 - 3x^2}{x^2} > 0$

$\implies (-1) \times \dfrac{1 - 3x^2}{x^2} < 0(-1)$

$\implies \dfrac{3x^2 - 1}{x^2} < 0$

$\implies \dfrac{(\sqrt{3}x +1)(\sqrt{3} -1)}{x^2} < 0$

Now by using wavy curve method :-

<-(-∞)-------(-1/√3)-----------(1/√3)-------(+∞)->

In interval

(1/√3) to (+∞) : value of expression is +ve

(-1/√3) to (1/√3) : value of expression is -ve

(-∞) to (-1/√3) : value of expression is +ve

So from above we can say that

In interval (-1/√3 , 1/√3) we will get the value of expression less than 0 (-ve)

So x Belongs to (-1/√3 , 1/√3)