Detailed reasoning must be shown in this question.
A researcher studying fluid dynamics determines that for any two positive flow rates uuu and vvv in a bifurcated pipe, the 'effective velocity' VeV_eVe and the 'total sum' SSS are defined as: Ve=u3+v3u2+v2andS=u+vV_e = \frac{u^3 + v^3}{u^2 + v^2} \quad \text{and} \quad S = u + vVe=u2+v2u3+v3andS=u+v
Use proof by contradiction to show that Ve<SV_e < SVe<S for all positive real numbers uuu and vvv.
By providing a counter-example, show that the statement in part (a) is not true for all real numbers uuu and vvv where u2+v2≠0u^2 + v^2 \neq 0u2+v2=0.
Practise Edexcel A Level Maths 1.1 Proof by Contradiction with exam-style questions for A Level Maths. 100 questions, matched to the Edexcel A Level Maths (9MA0) specification and written in Paper 1, Paper 2 and Paper 3 style. Every question includes a full worked solution and mark scheme, so you can see where marks are awarded rather than just whether you got the answer right.