Exclude custom taxonomy tag from loop

I have the following code at the beginning of a loop:

<?php query_posts('showposts=3&cat=84'); ?>
<?php $posts = get_posts('category=84&numberposts=3&offset=0'); foreach ($posts as $post) : start_wp(); ?>

I have a custom taxonomy called “display,” with a tag called “featured-slider.” In this loop, I want to include everything from category 84, but I want to exclude everything with a “featured-slider” value in the “display” taxonomy.

How would I rewrite the two lines above (query_posts and get_posts) to correctly exclude the custom taxonomy?

thank you

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I have rewritten the query_posts. As for get_posts you are better off using the WP_Query due to more control over the tax_query. Explained here.

<?php
$args = array(
    'cat' => 84,
    'posts_per_page' => 3,
    'offset' => 0,
    'tax_query' => array(
        'relation' => 'NOT IN',
        array(
            'taxonomy' => 'display',
            'field' => 'slug',
            'terms' => 'featured-slider'
        )
    )
);
$wpse42083_query = new WP_Query( $args );
while( $wpse42083_query->have_posts() ) : $wpse42083_query->the_post();
    // write post stuff in here
endwhile;

// Reset Post Data
wp_reset_postdata();
?>

Edit: I added the usage.