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tmua.me Tau Paper 1 · Q1

Paper 1Algebra

Pairwise distinct positive real numbers x,y,zx,y,z satisfy

1x+1y+1z=1,xyz=32.\frac1x+\frac1y+\frac1z=1, \qquad xyz=32.

Let

E=(x−y)2+(y−z)2+(z−x)2.E=(x-y)^2+(y-z)^2+(z-x)^2.

Which one of the following describes all the possible values of EE?

A8≤E≤60−2058\le E\le60-20\sqrt5
B8<E≤60−2058<E\le60-20\sqrt5
C8≤E<60−2058\le E<60-20\sqrt5
D8<E<60−2058<E<60-20\sqrt5
E0<E<60−2050<E<60-20\sqrt5

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