(7)
Find the greatest real number M such that the inequality
a^2 + b^2 + c^2 + 3abc ≧ M(ab + bc + ca)
holds for all nonnegative real numbers a, b, c satisfying a + b + c = 4.

(8)
Find the greatest real number M such that
(x＾2 + y^2)^3 ≧ M(x^3 + y^3)(xy - x - y)
for all real numbers x, y satisfying x + y ≧ 0.

(9)
Let a, b, c be nonnegative real numbers satisfying a^2 + b^2 + c^2 = 1. Prove that
sqrt(a + b) + sqrt(b + c) + sqrt(c + a) ≧ sqrt{ 7(a + b + c) - 3}

(10)
Prove that for all positive real numbers a, b, c satisfying a^2 + b^2 + c^2 + 2abc ≧1,
the following inequality holds:
1/a + 1/b + 1/c ≧ a/b + b/c + c/a + 2(a + b + c).

(11)
Find the greatest real number T satisfying
(x^2 + y)(x + y^2)/(x+y-1)^2 + (y^2 + z)(y + z^2)/(y+z-1)^2 + (z^2 + x)(z + x^2)/(z+x-1)^2 -2(x+y+z) ≧ T
for all real numbers x, y and z such that x+y≠1, y+z≠1, z+x≠1.

(12)
Show that for all nonnegative real numbers a, b, c satisfying a^2 +b^2 +c^2 ≦ 3 the following inequality holds:
(a + b + c)(a + b + c - abc) ≧ 2(a^2・b + b^2・c + c^2・a)

（*ﾟ∀ﾟ）=3ﾊｧﾊｧ