Question

suppose that y=a power x + a power –x ----------------------------------------- 2. which of the following may be correct? ​1)x=log power a(y+√y²–1)
2)x=log power a(y–√y²–1)
3) x=–log power a (y+√y²-1)
4)x=–log power a (y–√y²-1)
ans (multiple correct ans) in this u have to find two and wt is that?pls ans​

Answer 1

Step-by-step explanation:

given that y=a^x + a^-x

let a^x=u

so y=u+1/u

=> y=(u²+1)/u

=>uy=u²+1

or u²-uy+1=0

since in a quadratic ax²+bx+c=0

x=(-b±√(b²-4ac))/2a

so u=(y±√y²-4(1)(1))/2

=> u=(y+√y²-4)/2 or u=(y-√y-4)/2

since u=a^x therefore

a^x=(y+√y²-4)/2 or a^x=(y-√y²-4)/2

taking log on both sides we get

xloga=log((y+√y²-4)/2) or xloga=log((y-√y²-4)/2)

so

x=log base a ((y+√y²-4)/2) or

x=log base a ((y-√y²-4)/2)