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Suppose √9 − 8 cos 40◦ = a + b sec 40◦, where a and b are rational numbers. Then |a + b| equals?

Suppose √9 − 8 cos 40◦ = a + b sec 40◦, where a and b are rational numbers. Then |a + b| equals?

Grade:12th pass

2 Answers

Vikas TU
14149 Points
4 years ago
we can write --->
√9 − 8 cos 40◦ = a + b sec 40◦
as
√9 − 8 cos 40◦ = a + b /cos 40◦
Let cos40’ = t
then 
√9 − 8 t = a + b/t
squaring both sides,
and arranging after we get,
8t^3 + (a^2 -9)t^2 + 2abt + b^2 = 0
cos40 will have some constant numeric values,
comparing then coefficient of t^2 = R.H.S = 0
a^2 – 9 =0 
a = 3  or a = -3
coeff. of of t = 0 
2ab= 0
ab= 0
3b = 0  or -3b =0
b = 0

|a + b| = |3 + 0| or |-3 +0| = 3
is the answer.

 
GauRav Ginni
34 Points
4 years ago
Vikas yadav , according to answer key, right answer is 2 not 3 .
i’m also confused!               
 
any other method you have

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