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The equation x^4-3 x^3 = cos(3x)+3 has two real solutions on the interval from -10 to 10. Lets call these two solutions r and s. Use Mathematica's FindRoot command to find r and s. Now let M equal the sum of these two solutions, M=r+s. Enter the value for M in the space provided below.

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closed as off-topic by bobthechemist, Mr.Wizard Jan 28 at 5:52

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If this is a homework/class problem, might want to mark it as such. –  rasher Jan 28 at 2:32
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This question appears to be off-topic because it is about entering "...the value of M in the space below" but no space is provided. (Or a snarky way of stating that the OP needs to provide some effort when asking others to do homework questions for them.) –  bobthechemist Jan 28 at 4:44
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2 Answers 2

Using ErsekRootSearch package

Needs["Ersek`RootSearch`"]
f[x_] := x^4 - 3 x^3 - Cos[3 x] - 3;
soln = x /. RootSearch[f[x] == 0, {x, -10, 10}]
(*  {-0.831448, 3.06992} *)

Total[soln]
(* 2.23848 *)

You need to edit the RootSearch.m first and change $MinPrecision=-Infinity to $MinPrecision=Infinity (there are about 5-6 places) this is because the package is old and was not updated at MathSource.

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First, let's plot both graphs to get an idea of their points of intersection

Plot[{x^4 - 3 x^3, Cos[3 x] + 3}, {x, -3, 4}, Filling -> {1 -> {2}}]

Mathematica graphics

We see that the intersections are around -1 and 3. Then using FindRoot we get:

{r, s} = x /. FindRoot[x^4 - 3 x^3 == Cos[3 x] + 3, {x, #}] & /@ {-1, 3}

{-0.831447617, 3.06992283}

Total[{r, s}]

2.23847521

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1  
But have you entered "the value for M in the space provided below"? Sometimes I wonder if Mathematica can generate "the space below". –  bill s Jan 28 at 3:43
    
@bills I'm working on it :) –  RunnyKine Jan 28 at 4:24
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