If a2 + b2 + c2 = x2 + y2 + z2 = 1, then ax + by + cz is

1) > 1

2) < 1

3) > 0

4) < 0

Solution: (2) < 1

Since AM > GM

[a2 + x2] / 2 > √a2x2

[a2 + x2] > 2ax

[b2 + y2] > 2by

[c2 + z2] > 2cz

a2 + x2 + b2 + y2 + c2 + z2 > 2 (ax + by + cz)

(a2 + b2 + c2) + (x2 + y2 + z2) > 2 (ax + by + cz)

1 + 1 > 2 [ax + by + cz] [ax + by + cz] < 1

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