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How to find $x$?

The issue I have here is that $x$ is there even on the RHS.

If you could help it would be really nice as I have a test tomorrow.

2 Answers2

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Answering this as an answer since I don't have enough reputation to comment:

What is the solution of cos(x)=x? is similar to this question, and as the majority of answers point out, there is no solution in terms of standard functions, however you can prove it has solutions using IVT.

latbbltes
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Write the equation as $1+\frac x 4= cosx$ and draw the graph $y=1+\frac x 4$ and $y= cosx$, on the same figure you get three point of intersection. The values of $x$ are at the point of intersection of these two curve where one is zero and another two you have to find numerically or a given range.

SAHEB PAL
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