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Guide and features
Guide and features
Science, Technology, Engineering and Mathematics
Featured Early Years Foundation Stage; US Kindergarten
Featured UK Key Stage 1&2; US Grades 1-5
Featured UK Key Stage 3-5; US Grades 6-12
Featured UK Key Stage 1, US Grade 1 & 2
Featured UK Key Stage 2; US Grade 3-5
Featured UK Key Stages 3 & 4; US Grade 6-10
Featured UK Key Stage 4 & 5; US Grade 11 & 12
When you meet a class of equations like this it would be good to find a general formula involving $a$ and $b$ (like the formula for solutions of quadratic equations).
It often helps towards a general solution to try special cases as suggested in this problem and exact solutions can be found in special cases. More generally however there is no closed formula for solutions and you will need to find approximate solutions by numerical methods.
This problem involves the use of logs, solving a quadratic equation and using a numerical method such as interval halving or the Newton Raphson method. To speed up the process of solving this equation for a particular pair of values of $a$ and $b$ you can use a programmable calculator or a spreadsheet.
Newton Raphson Method
Approximate solution by numerical methods.
Trigonometric functions and graphs
Powers & roots
Meet the team
The NRICH Project aims to enrich the mathematical experiences of all learners. To support this aim, members of the NRICH team work in a wide range of capacities, including providing professional development for teachers wishing to embed rich mathematical tasks into everyday classroom practice. More information on many of our other activities can be found here.
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