# If a and b are two real roots of the equation ( k + 1) tan^x - 2^1/2 p tanx = 1 - k and p are real no .if tan^ (a + b) = 50 then the value of p is .

Solution

( k +1 ) tan^2 x - 2^1/2 p tanx = 1 - k

tan^2 (a + b) = 50

Now ,

⇒    tan a + tan b = 2^1/2 p / p + 1   ,    tan a  tan b  =( p - 1) / ( p + 1)

⇒ [  ( 2 ^ 1/ 2 p)  / ( k + 1) / 1 - ( k -1)  /( k + 1) ]

⇒  2 p^2 / 4 = 50

⇒   p^2 = 100

⇒   p =10  Ans

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