Should we square the number?

Algebra Level 1

If P ≥ − 2 P \geq -2 and Q ≥ − 3 Q \geq -3 , is it true that the minimum value of P × Q P \times Q is 0?

No, it is not true Yes, it is true

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Pi Han Goh by Pi Han Goh , 30, Malaysia

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2 solutions

We can get a smaller value.Eg: P = − 2 , Q = + 3 ⟹ P Q = − 6 < 0 P=-2,Q=+3\implies PQ=-6<0

Infact there is no minimum value for P Q PQ .We can easily see this by setting P = − 2 , Q = k > 0 P=-2,Q=k>0 .Then it is clear that P Q = − 2 k PQ=-2k keeps on decreasing as the value of k k keeps on increasing.

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P = -3, Q=1, P*Q=-3, -3<0

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