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Question

If f(x)=x2+2bx+2c2 and g(x)=x22cx+b2 are such that the minimum value of f(x) always exceeds maximum value of g(x), then which of the following is/are correct?

A
b=1, c=0
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B
b=2, c=3
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C
b=3, c=5
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D
b=4, c=5
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Solution

The correct option is C b=3, c=5
f(x)=x2+2bx+2c2
=(x+b)2+2c2b2
g(x)=x22cx+b2
=(x+c)2+b2+c2

Given that
min[f(x)]>max[g(x)]
2c2b2>b2+c2
c2>2b2 (1)
Clearly, option (b) and (c) are satisfying equation (1)

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