A student tries to solve 𝑥 2 +3𝑥=50 as follows Discuss: What has the student done to get from the equation to line 1 and from line 1 to line 2? Why is this not the answer?

A student tries to solve 𝑥 2 +3𝑥=50 as follows 𝑥 2 =50−3𝑥 𝑥= 50−3𝑥 The solution will be a value of 𝑥 that when substituted into the equation gives the value of 𝑥 used

To speed this process up we can use the ANS button as follows… Let’s start with 0… 𝑥 1 =0 𝑥 2 = 50−3×0 =7.071… 𝑥 3 = 50−3×7.071… =5.365… 𝑥 4 = 50−3×5.365… =5.823… To speed this process up we can use the ANS button as follows… 𝑥 4 = 50−3×𝐴𝑁𝑆 =5.704… 𝑥 5 = 50−3×𝐴𝑁𝑆 =5.735… 𝑥 6 = 50−3×𝐴𝑁𝑆 =5.727… 𝑥 7 = 50−3×𝐴𝑁𝑆 =5.729… What do you notice?

The values of 𝑥 𝑛+1 is getting closer the value of 𝑥 𝑛 𝑥 4 = 50−3×𝐴𝑁𝑆 =5.704… 𝑥 5 = 50−3×𝐴𝑁𝑆 =5.735… 𝑥 6 = 50−3×𝐴𝑁𝑆 =5.727… 𝑥 7 = 50−3×𝐴𝑁𝑆 =5.729… The values of 𝑥 𝑛+1 is getting closer the value of 𝑥 𝑛 A solution is 𝒙=𝟓.𝟕𝟑 𝟐 𝒅𝒑

Javed is solving a problem and needs to know the solutions of the equation 5𝑥 2 −3𝑥−4=0. He plans to use an iteration. Javed decides to use the iterative formula 𝑥 𝑛+1 = 3 𝑥 𝑛 +4 5 Using 𝑥 0 =5 Find a solution to Javed’s equation to 2 decimal places. Whiteboards

Javed decides to use the iterative formula 𝑥 𝑛+1 = 3 𝑥 𝑛 +4 5 Using 𝑥 0 =5 Find a solution to Javed’s equation to 2 decimal places. 𝑥 1 = 3×5+4 5 =1.9493588869.. Whiteboards 𝑥 2 = 3×𝐴𝑁𝑆+4 5 =1.403492842…

In your books: 1. 2. 3.

Challenge Acknowledgements: Further Questions available from https://allaboutmaths.aqa.org.uk/attachments/5309.pdf