Need help with graphs

**Andy005** · 11 Mar 2018, 3:24 PM

Sketch the graph y=(x+1)^4/x^4+1. Use this graph to find the set of values of the real number k for which the equation (x+1)^4=k(x^4+1) has two real distinct roots.

I sketched the graph, but I don't understand what I should do after.

Thanks for your assistance.

**fan96** · 11 Mar 2018, 3:39 PM

$(x+1)^4 = k(x^4+1)$

$\frac{(x+1)^4}{x^4+1} = k$ (This equation is equivalent to the one before it, because $(x^4+1) > 0$ for all $x \in \mathbb{R}$ .

If this equation has two distinct real roots, what could be said about the graphs of

$y = \frac{(x+1)^4}{x^4+1}\, $and$\, \,y = k\, $?$$

Spoiler (rollover to view):

Consider the intersections of the graphs.