# Thread: Need help with graphs

1. ## Need help with graphs

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.

2. ## Re: Need help with graphs

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

$\frac{(x+1)^4}{x^4+1} = k$ (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.

3. ## Re: Need help with graphs

Find the values for y=k intersects the graph $\frac{(x+1)^4)}{x+1}$ two times (you can do this visually)

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