Apporoaches to solve the given algebraic expression If

Sara Kelley

Sara Kelley

Answered question

2022-03-15

Apporoaches to solve the given algebraic expression
If   x4 + x2 = 115 then what is the value of the given expression
(x+1x-1)13+ (x-1x+1)13 =  ?

Answer & Explanation

Cohen Hunt

Cohen Hunt

Beginner2022-03-16Added 4 answers

Let a=(x+1x-1)13+ (x-1x+1)13.
Notice that the first term is the multiplicative inverse of the second term. Thus
a3=x+1x-1+x-1x+1+3((x+1x-1)13+ (x-1x+1)13).
So a3-3a=x+1x-1+x-1x+1.
You can calculate the right hand side and then solve for a.

Pentyrch9ci

Pentyrch9ci

Beginner2022-03-17Added 9 answers

We have putting t=tan(x12)
cos(x1)=1t21+t2
It's the Weierstrass substitution
Putting y=t2 we get:
cos(x1)=1y1+y
Now we put x=y to get:
(-cos(x1))13+(-1cos(x1))13=?
After that I have tried cos(3x)=4cos3(x)3cos(x)

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