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2 marksThe Real Number System – ℝ

CAPE Pure Mathematics Unit 1 · May/June 2009 · Paper 2 · Question 1(b)(iii)

Let x and y be positive real numbers such that x ≠ y.

Deduce that (y+1)⁴ - y⁴ < 4(y + 1)³.

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Other parts of this question

  1. 1(a)Without the use of tables or a calculator, simplify √28 + √343 in the form k√7, where k is an integer.[5 marks]
  2. 1(b)Simplify (x⁴ - y⁴) / (x - y).[6 marks]
  3. 1(b)(ii)Hence, or otherwise, show that (y+1)⁴ - y⁴ = (y+1)³ + (y+1)²y + (y+1)y² + y³.[4 marks]
  4. 1(c)Solve the equation log₂ x = 1 + log₂ 2x, x > 0.[8 marks]

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