Power of 2

Number Theory Level pending

True or False?

If \(x_1, x_2 , \ldots , x_n\) are positive numbers satisfying \[ (1+x_1)(1+x_2)(1+x_3)\cdots(1+x_n) \geq 2^n , \] then \( \sqrt{x_1x_2x_3 \cdots x_n} \) must be equal to 2.

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