IB Maths AA HL AA 1.3 practice question

Paper 1, no calculatorHard6 marks

For real numbers $u,v,w$ it is given that $u+v+w=0$ and $uvw=5$

(a)

Write down the value of $u+v+w$

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(b)

For arbitrary real numbers $u,v,w$ starting with the left-hand side, prove that

u^3+v^3+w^3-3uvw \equiv (u+v+w)(u^2+v^2+w^2-uv-vw-wu).

In your final line, use $\equiv$ to indicate an identity.

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(c)

Hence determine $u^3+v^3+w^3$ for the numbers in the stem.

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