Question

If 2cos^2Φ-11cosΦ+5=0, then find possible values of cosΦ.​

Answer 1

Answer:

Use Mid term splitting method:

2 cos^2 Φ - 11 cos Φ + 5 = 0

2 cos^2 Φ - 10 cosΦ - cosΦ + 5 = 0

2 cos Φ( cosΦ - 5) - 1 ( cos Φ - 5) = 0

( cosΦ - 5) ( 2cos Φ - 1 ) = 0

Cos = 5, 1/2

Answer 2

2cos²(phi) - 11cos(phi) + 5 =0

let x = cos (phi)

then,

2x² - 11x +5=0

2x² - (10+1)x +5=0

2x² - 10x - x + 5= 0

2x(x-5)-1(x-5) =0

(2x-1)(x-5) = 0

Either 2x -1=0

hence, x = 1/2

or, x-5=0

hence, x=5

Thus, cos (phi) = 1/2, 5

but maximum value of cos (phi) is +1, hence we take cos(phi)=1/2..