The number of pairs (a, b) of positive real numbers satisfying `a^(4)+b^(4)lt1" and "a^(2)+b^(2)gt1` is

Options

A. 0
B. 1
C. 2
D. more than 2

Answer

D

Explanation

Let `a^(2)=3" & "b^(2)=N" then "mgt 0 " and "N gt 0`
Now given condition is `M+Ngt1" and "m^(2)+N^(2)lt1`

(M,N) lies inside circle `x^(2)+y^(2)lt1" and above line "x+ygt1`
`rArr(M, N)` lies shaded region and number of points in shaded refion are infinite, so number of pair (a, b) are also infinite.