The number of pairs (a, b) of positive r...

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

A

0

B

1

C

2

D

more than 2

Text Solution

Verified by Experts

The correct Answer is:

D

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.

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