Clavis TMUA Set A Paper 2 · Question 6

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Clavis TMUA Set A Paper 2 · Q6

Paper 2Logic & proof

Consider the following statement $(*)$ about a real constant $k$ :

$(*)$ There exists a real number $x$ such that, for all real numbers $y$ ,

x^2+y^2\geq kxy.

What is the complete set of values of $k$ for which $(*)$ is true?

-2\leq k\leq2

-1\leq k\leq1

k\geq0

k=0

only

Eall real values of

k

Fthere are no such values of

k

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