Bunuel wrote:

The value of \(−3 + \sqrt{9−k}\) is positive for which of the following values of k ?

I. -1

II. 0

III. 1

A. None

B. I only

C. II only

D. III only

E. I and III

Given Expression = \(-3 + \sqrt{9 - k}\)

If k = 1

Given Expression = \(-3 + \sqrt{8}\)

We know that \(\sqrt{9} = 3\). So \(\sqrt{8}\) will be a little less than 3.

Given Expression = -3 + Something less than 3 = A little negative quantity

If k = 0

Given Expression = \(-3 + \sqrt{9}\)

Given Expression = \(-3 + 3\) = 0 = A non-negative non-positive quantity

If k = -1

Given Expression = \(-3 + \sqrt{10}\)

We know that \(\sqrt{9} = 3\). So \(\sqrt{10}\) will be a little more than 3.

Given Expression = -3 + Something more than 3 = A little positive quantity

It is positive only for k = -1

Answer B.

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