1.4.1 Structure and methods of proof

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Question 60

Detailed reasoning must be shown in this question.

A researcher studying fluid dynamics determines that for any two positive flow rates $u$ and $v$ in a bifurcated pipe, the 'effective velocity' $V_e$ and the 'total sum' $S$ are defined as:

V_e = \frac{u^3 + v^3}{u^2 + v^2} \quad \text{and} \quad S = u + v

Use proof by contradiction to show that $V_e < S$ for all positive real numbers $u$ and $v$ .

[4]

By providing a counter-example, show that the statement in part (a) is not true for all real numbers $u$ and $v$ where $u2+v2≠0u^2 + v^2 \neq 0$ .

[2]

1.4.1 Structure and methods of proof Questions

A Level
Maths
1.4.1 Structure and methods of proof

A Level
Maths AQA
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