KVPY 2015 #1

Algebra Level 4

If z is a complex number satisfying ∣ z 3 + z − 3 ∣ ≤ 2 \displaystyle | z^3 + z^{-3} | \leq 2 , then maximum possible value of ∣ z + z − 1 ∣ . \displaystyle | z + z^{-1}|.

More KVPY Question

2 2 2 3 \sqrt[3]2 1 1 2 2 2\sqrt2

Akhil Bansal by Akhil Bansal , 22, India

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1 solution

Rajdeep Brahma
Jan 9, 2018

Use a^3+b^3=(a+b)(a^2-ab+b^2)...then use am>gm...

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