If `f(x)=x^2+2bx+2c^2`, `g(x)=-x^2-2cx+b^2` and `minf(x)>maxg(x)` then

Options

A. `abs(b)lt2abs(c )`
B. `abs(c)lt2abs(b )`
C. `abs(c )gtsqrt2abs(b )`
D. `abs(b )gtsqrt2abs(c )`

Answer

3

Explanation

`f(x) =(x+b^(2))^(2)+2c^(2)- b^(2)`
`rArrf_(min)=2c^(2)-b^(2)`
g(x)=-`(x+c)^(2)+c^(2)+b^(2)`
`rArrg_(max)=c^(2)+b^(2)`
`f_(min)gtg_(max)`
`rArr2c^(2)-b^(2)gtc^(2)+b^(2)`
`rArrc^(2)gt2b^(2)`
`rArrabs(c )gtsqrt2abs(b)`