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2026 NYGH P2 Q4

2026 NYGH P2 Q4

IP 4
4 marks
  1. Show that the expression \(2x^2-4x+5\) is always positive for all real values of \(x\).[2]
  2. Hence, solve the inequality \(\dfrac{x^2-1}{2x^2-4x+5}>0\).[2]

Solution:

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Answer:(a) \(2x^2-4x+5=2(x-1)^2+3>0\) (b) \(x<-1\) or \(x>1\)

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