>>101

A.556. (s)
　Prove that for arbitrary real numbers a_1, a_2,･････, a_n there exist a real t such that
　　Σ[i=1,n] |sin(t-a_i)| ≦ 1/tan(π/2n).

A.561. (s)
　Show that
　　(a^3)b/(3a+b)^p + (b^3)c/(3b+c)^p + (c^3)a/(3c+a)^p
　　　　　≧ (a^2)bc/(2a+b+c)^p + (b^2)ca/(2b+c+a)^p + (c^2)ab/(2c+a+b)^p
　holds for all positive numbers a,b,c,p.

A.563. + B.4461.
　Let 1≦p<2 be a real number.　Prove that
　(x+y)^p + (X+Y)^p + (x+Y)^p + (X+y)^p ≦ x^p + y^p + Y^p + X^p + (x+y+Y+X)^p,
　for all non-negative real numbers x,y,Y & X.

B.4417. (s)
　Solve the equation　sin(x) + (1/2)cos(x) = {sin(x+45ﾟ)}^2

B.4427. (s)
　Show that if α,β and γ are the angles of a triangle, then
　　(sinα + sinβ + sinγ)^2 > 9(sinα)(sinβ)(sinγ).

B.4433.
　Solve the equation　(1+x)^8 + (1+x^2)^4 = 82x^4.

(s) は解あり。