Question

If x be real then minimum value of f(x) = x2 + 2bx + 2c2 is greater than the maximum value of g(x) = – x2 – 2cx + b2 for...

Answer 1

Given f(x) = x2 + 2bx + 2c2

= (x + b)2 + (2c2 – b2)

Thus, the min value of f(x) is (2c2 – b2)

Also, g(x) = – x2 – 2cx + b2

= b2 + c2 – (x + c)2

Thus, the max value of g(x) is 2b2

Given condition is,

Min value of f(x) > max value of g(x)