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Algebraic Methods

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Question 81
a.

Show that

4a2−4ab+b2=(2a−b)2 4a^2-4ab+b^2=(2a-b)^2 4a2−4ab+b2=(2a−b)2
[1]
b.

Hence prove that for positive values of a a\,a and bbb

4ab+ba≥4 \frac{4a}{b} + \frac{b}{a} \geq 4 b4a​+ab​≥4
[3]
c.

Prove, by counter example, that this is not true for all values of a a\,a and bbb.

[2]
Markscheme

Algebraic Methods Questions

  1. A Level
  2. /Maths
  3. /Algebraic Methods

257 exam-style questions on Edexcel A Level Maths Algebraic Methods, covering 7.1 Algebraic Fractions, 7.2 Dividing Polynomials, 7.3 The Factor Theorem, 7.4 Mathematical Proof, and 7.5 Methods of Proof. Each one has a worked solution and a mark scheme showing where the marks go.

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