Question 4 15 marks You should use algebra in all parts of this question, showing your working clearly. (a) Solve the following equations, giving vour answers as integers, fractions or surds in their simplest form where necessary. (i) 12r-8=T72-8 (i) 17+6(Jr-H=3% -2z x 3 1 (iii) + = _ 2r4+1 22-1 2 (iv) 9a2 = 2Ta You have learnt about solving quadratic equations using the following methods: . factorising . the guadratic formula completing the square Explain which method you would use to solve the following equation: z? - 122+ 9=0. There is no need to solve the equation. Artificial intelligence (Al) programs such as ChatGPT are known to make the same mathematical mistakes as people commonly do, as they draw on input created by people. An Al program was asked to rearrange the formula 2 ~13af=3f+5(6 J;) to make f the subject (assuming that 36 2c 0). The AT's incorrect attempt is shown below. 2c f 13af=3f+(6-5% i =Sl Clear the fractions by multiplying by 3 39a-3f=9f+2c(6- f) Multiply cut the brackets [2] Multiply out the brackets 39a - 3f =9f + 12c + 2cf Collect the f terms -39a - 12c =9f +3f +2cf -39a - 12c = 12f + 2cf 39a - 12c = f(12 + 2c) Divide by 12 + 2c to give -39a - 12c = 12 + 2c (i) Write out a correct rearrangement of the formula. [3] (ii) Identify and explain two of the mistakes the AI has made. [1]