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Question

If a2+b2+c2=1, then ab + bc + ca lies in the interval


A
(1, 2)
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B
[0,12)
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C
[12,1]
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D
[0, 1]
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Solution

The correct option is B [12,1]
a2+b2+c2abbcca=12(ab)20
or 1ab0ab1(1)
(a+b+c)2=a2+2ab=1+2ab0
ab12(2)
Hence from (1) and (2), (ab) lies in [12,1].

Mathematics

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