Find the exact positive solution for: x (x + 6 )= 91 using trial and improvement method
Answers
Answer:You might need to use this method if you are asked to solve an equation where there is no exact answer. You may also be asked to give the solution to a given number of decimal places or significant figures. The question should indicate the degree of accuracy required.
For a quick recap on rounding see our section Approximation.
Example
Find the answer to the equation \(x^3 – 2x = 25\) to one decimal place.
Solution
We are looking for a number to replace \(x\), that when applied to the equation will give us 25. Start by guessing what \(x\) could be, then refine your answer based on your result. Set it out like this.
First we'll try: \(x = 3\)
\[3^3 - (2 \times 3)\]
\[27 - 6\]
\(= 21\); too small
Second try: \(x = 4\)
\[4^3 - (2 \times 4)\]
\[64 - 8\]
\(= 56\); much too high
We could use a number half way between 3 and 4, but our first tries suggest it will be closer to 3.
Third try: \(x = 3.2\)
\[3.2^3 - (2 \times 3.2)\]
\[32.768 - 6.4\]
\(= 26.368\); too high
Fourth try: \(x = 3.1\)
\[3.1^3 - (2 \times 3.1)\]
\[29.791 - 6.2\]
\(= 23.591\); too small
This means the answer lies between 3.1 and 3.2.
Step-by-step explanation: