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SPM Additional Mathematics 2019, Paper 2 (Question 2)


Question 2:
Express 2n + 2 – 2n + 1 + 2n – 1 in the form p(2n – 1), where p is a constant.
Hence, solve the equation 8(2n + 2 – 2n + 1 + 2n – 1) = 5(2n2).
[6 marks]


Solution:

2n+22n+1+2n1=(2n×22)(2n×21)+(2n÷21)=2n(42+12)=2n(52)=5(2n2)=5(2n1)p=5

8(2n+22n+1+2n1)=5(2n2)8(5)(2n1)=5(2)n223×2n1=2n23+n1=n2n2n2=0(n+1)(n2)=0n=1  or  n=2

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