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The number of pair (x,y) satisfying 4x 2 -4x+2=sin 2 y and x 2 +y 2 ≤3 are a.0 b.2 c.4 d.none of these

The number of pair (x,y) satisfying 4x2-4x+2=sin2y and x2+y2≤3 are


a.0


b.2


c.4


d.none of these

Grade:12th Pass

1 Answers

Ashwin Muralidharan IIT Madras
290 Points
10 years ago

Hi Menka,

 

Please note the minimum value that the Q.Expression can take is 1 (when x=1/2).

So y^2 ≤ 3-1/4 = 11/4.

 

and for this sin^2 y = 1, so y = Π/2, -Π/2.

So there are two pairs viz. (1/2,Π/2) and (1/2,-Π/2)

 

Hence Option (B).

 

Hope that helps.

 

Best Regards,

Ashwin (IIT Madras).

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