KVPY SA Exam 19-Nov-2017 Question Paper

Question : 3 of 80

Marks: +1, -0

If a,b,c are real numbers such that a + b + c = 0 and

a_2 + b_2 + c_2 = 1

, then

(3a + 5b -8c)^2 + (–8a + 3b + 5c)^2

+ (5a -8b + 3c)^2

is equal to

Solution:

Expanding are get

98 (a^2 + b^ 2 + c^2 ) -98 (ab + bc + ca)

= 98 -98(-1/2)

= 147

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