Update on "user" and "technicien" with one to one connection

I have two tables user and technician with one to one connection, technician inherits from user. After editing technician information through edit form and saving no update happens on tables user and technician. and no errors as well.Here is my code Could anyone help me with this, please ? Thank you for the attention you give to my question and for not judging me.

Controllers

public function edit($id)
{
    $technicien=technicien::find($id);
    $user = $technicien->user;
    return view('technicien.edit',['technicien'=>$technicien])->with('user',$user);
}

public function update(Request $request, $id)
{
    // do some request validation

    $technicien=technicien::find($id);
    $technicien->update($request->all());
    $technicien->user->update($request->get('user'));
    $user->nom = $request->update('nom');

    return redirect('/technicien');
    }

View

 @extends('Layouts/app')
 @extends('Layouts.master')
 @section('content')
<div class="container">
    <div class="row">
        <div class="col-md-10">
            <h1>Modifier Technicien</h1>
        <form action="" method="update">
        
        


             <div class="form-group">
            <label for="nom">Nom</label>
            <input id="nom" type="text" class="form-control" name="user[nom]" value="" >
        </div>
        <div class="form-group">
            <label for="prenom">Prenom</label>
            <input id="prenom" type="text" class="form-control" name="user[prenom]" value="" >
        </div>
        <div class="form-group">
            <label for="prenom">Email</label>
            <input id="prenom" type="text" class="form-  control" name="user[email]" value="" >
        </div>

        <div class="form-group">
            <label for="">moyenne Avis</label>
            <input type="text"  name="moyenne_avis" class="form-control" value ="" >
        </div>
        <div class="form-group">
            <label for="">Etat Technicien</label>
            <input type="text"  name="actif" class="form-control" value ="" >
        </div>

        <div class="form-group">
            <input type="submit" value="enregistrer"        class="form-control btn btn-primary">
        </div>
            </div>




        </form>
    </div>
</div>
@endsection

Route.php

Route::get('/technicien/{id}/edit', 'TechnicienController@edit'); Route::patch('/technicien/{id}', 'TechnicienController@update')->name('technicien.update');

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