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)