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Maths Puzzle
Numerical Ability
For all a,b,c,d>0 a+b+c+d=4
prove (1/a^2) + (1/b^2) + (1/c^2) + (1/d^2) ≥ a^2 + b^2 + c^2 +d^2
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1=1
2=8
3=27
4=64
5=?
For all a,b,c≥0 and a+b+c = 3
Prove that (ab^3 + bc^3 + ca^3)(ab+bc+ca) ≤ 16