Q3

Algebra Level 3

Number of integral solutions of $\frac { x+2 }{ { x }^{ 2 }+1 } >\frac { 1 }{ 2 }$ is :

3 1 0 2

3 solutions

Maninder Dhanauta
Oct 16, 2015

I hope this is a clear solution

We can also use wavy curve method in the inequality to obtain the range..

Sagar Shah - 5 years, 2 months ago

@sagar shah Exactly what is this wavy curve method?

Maninder Dhanauta - 5 years, 2 months ago

Refer to this wiki.. https://brilliant.org/wiki/wavy-curve-method/

Sagar Shah - 5 years, 1 month ago

Atul Shivam
Oct 17, 2015

Solving the inequality we will get range of x from (-1,3) so total integers in between this will be 0,1,2 and that's the answer ie. 3 integral solutions

Vinayak Srivastava
Jul 8, 2020

$\dfrac{x^2}{x^2+1}>\dfrac{1}{2}$

Cross-multiplying(since no real $x$ can have $x^2+1=0$ ),

$x^2-2x-3 <0$ $(x-3)(x+1)<0$ $\implies x \in [0,2]$ We need integer values of $x$ $\implies x\in \{0,1,2\}$ $\text{No. of values}=\boxed{3}$

Q3

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