Logarithms and equations question

[astonky]

Hey everyone,

Could you please help me on the following question?

Solve the following system of equations.

log_x+1y = 2

log_y+1x = 1/4

I understand how to start

ie. (x+1)²=y

(y+1)=x⁴

Then, (x+1)²= x⁴-1

Can you explain the steps I need to do next to solve the equation. I found the answers, but I don't understand how anyone would procede from where I stopped.

x = −1, not possible
x =1.70, y = 7.27

 

Thanks for your help

 

[kw0573]

I plugged in (x + 1)² = X⁴ - 1 into an online equation calculator and the 2 real roots are -1 and a really complex expression. Since cubic equation formula is not part of syllabus, I think they just want you to find the zeros graphically. 

https://www.wolframalpha.com/input/?i=(x%2B1)^2%3D+x^4-1

Edited October 16, 2016 by kw0573

[IBTopper]

Yes, as kw0573 said, you can sketch a graph of it on your paper. I am assuming it is Paper 2 (since you used a calculator), so you can definitely first simplify the expression (like you did) and then sketch the graph, clearly showing/highlighting all the intersection points (solutions to the system). 

Hope this helps