>>72
crux/v44/n1/Problems_44_1

4304
Evaluate
cot(π/7) + cot(2π/7) + cot(4π/7) + {cot(π/7)}^3 + {cot(2π/7)}^3 + {cot(4π/7)}^3,

4306-改
Prove that
　　√(16n+24) > √n + √(n+1) + √(n+2) + √(n+3) > √(16n+20),

4308.
Let a,b & c be positive real numbers. Prove that
　 27abc(aab+bbc+cca) ≦ (a+b+c)^2･(ab+bc+ca)^2,

4309.
Let a,b & c be real numbers such that a+b+c=3. Prove that
　　2(a^4 + b^4 + c^4) ≧ ab(ab+1) + bc(bc+1) + ca(ca+1).