# Increasing the accuracy of residue in FindRoot

I have solved a system of non-linear equations with findRoot. I tried to avoid inexact coefficients and also assign a high working precision. This is my snippet:

rho0=1.0; rho1=1.0;rho2=10^(-5);rhoint=10^(0);lambdaD=210;

• You do use inexact numbers when you set rho0=1.0; rho1=1.0;. Better use rho0 = 1; rho1 = 1; instead. Then you may also use FindRoot[fr,[...]] instead of FindRoot[frprecise,[...]]. – Henrik Schumacher Mar 30 '19 at 20:17
• Your system of equations can be solved by Solve as well. If you use exact input (e.g., use rho0 = 1; rho1 = 1 as recommended by @Henrik), then you will get an exact answer that you can numericize to any desired precision. – Carl Woll Mar 30 '19 at 20:32
{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5572501420974731, "perplexity": 1300.654678086768}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-29/segments/1593655886178.40/warc/CC-MAIN-20200704135515-20200704165515-00107.warc.gz"}