Question 4 - 15 marks You should use algebra in all parts of this question, showing your working clearly. (a) Solve the following equations, giving your answers as integers, fractions or surds in their simplest form where necessary. (i) 12x -8 =72 - 8x [2] (ii) 17 + 6( -1 -4) = 4 - 2x [2] 3 (iii) 2r + 1 [3] 21 - (iv) 9a? = -27a [2] (b) You have learnt about solving quadratic equations using the following methods: factorising the quadratic formula completing the square Explain which method you would use to solve the following equation: x2 - 12x + 9 = 0. There is no need to solve the equation. [2] (c) 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 AI program was asked to rearrange the formula -13a - f = 3f + 2(6 - to make f the subject (assuming that 36 - 2c / 0). The Al's incorrect attempt is shown below.-13a - f = 3f + 3(6 - 3 Clear the fractions by multiplying by 3 -39a - 3f = 9f +2c(6 - f) Multiply out the brackets -39a - 3f = 9f + 12c + 2cf Collect the f terms -39 a - 12c = 9f + 3f + 2cf -39a - 12c = 12f + 2ef -390 - 12c = f(12 + 2c) Divide by 12 + 2c to give -39 a - 12c f = 12 + 2c (i) Write out a correct rearrangement of the formula. (ii) Identify and explain two of the mistakes the AI has made. page 7 of 11