4

Part of 2004 Irish Math Olympiad

Problems(2)

Only two real roots

Source: Ireland 2004

Prove that there are only two real numbers

x

(x-1)(x-2)(x-3)(x-4)(x-5)(x-6) = 720

Functions question

Source:

Define the function

m

of the three real variables

x

y

z

m

x

y

z

x^2

y^2

z^2

x

y

z

R

.
Determine, with proof, the minimum value of

m

x

y

z

R

subject to the following restrictions:

x

y

z

x^2

y^2

z^2