已知x,y,z,均大于0,求证x²/a+y²/b+z²/c≥(x+y+z)²/(a+b+c)

Question

已知x,y,z,均大于0,求证x²/a+y²/b+z²/c≥ (x+y+z)²/(a+b+c)

Answer 1

(a+b+c)(x²/a+y²/b+z²/c)≥(x+y+z)²
所以(x²/a+y²/b+z²/c)≥(x+y+z)²/(a+b+c)
柯西不等式