exam Maths Puzzle Numerical Ability

I can't figure out questions 7, 11, 19, 21, 27 on page 259.

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exam Other Question

a. Let a,b,c be three distinct positive real numbers.
1) Prove that a^3+b^3>a^2b+b^2a.
2) Write down, without proving them, similar inequalities for (a^3+c^3) and (b^3+c^3).
3) x^2+3=-24