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+2 votes
5.2k views
in Mathematics by (150k points)

If a, b, c are distinct +ve real numbers and a2 + b2 + c2 = 1 then ab + bc + ca is

(a) less than 1 

(b) equal to 1

(c) greater than 1 

(d) any real no.

1 Answer

+2 votes
by (87.2k points)
selected by
 
Best answer

(a) : In such type of problem if sum of the squares of number is known and we needed product of numbers taken two at a time or needed range of the product of numbers taken two at a time. We start square of the sum of the numbers like
(a + b + c)2 = a2 + b2 + c2 + 2(ab + bc + ca)
=> 2(ab + bc + ca) = (a + b + c)2 – (a2 + b2 + c2)

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