+0  
 
+1
32
3
avatar

If \(t + \frac{1}{t} = 3\) ,then what is \(t^5 + \frac{1}{t^5}\)?

 Mar 28, 2021
 #1
avatar+228 
0

Easy, if you know the formula. wink

Hint:

x^5 + y^5 = ?

 

If you still don't know, please reply!

 Mar 28, 2021
 #2
avatar
+1

No I don't. Please Explain. Thank you!

Guest Mar 28, 2021
 #3
avatar+228 
0

  t^5 + 1/t^5 = (1 + 1/t)(t^4 - t^3 * 1/t + t^2 * 1/t^2 - t * 1/t^3 + 1/t^4)

= (t + 1/t)(t^4 + 1/t^4 -(t^2 +1/t^2) + 1)

 

Lets stop there,

 

Now we need to find t^4 + 1/t^4 and t^2 + 1/t^2wink

 

 

t^2 + 1/t^2 = (t + 1/t)^2 - t * 1/t

t^2 + 1/t^2 = 3^2 - 1

= 9 - 1 = 8

 

t^4 + 1/t^4:

 

(t^2 + 1/t^2)^2 = t^4 + 2 + 1/t^4

Soo, t^4 + 1/t^4 = 8^2 - 2

t^4 + 1/t^4 = 64 - 2 = 62

 

Now we can plug this back!

 

 

(t + 1/t)(62 - 8 + 1) = 3 * 55 = 165

wink

I love these types of questions and I kinda just reviewed this yesterday!laugh

I hope you understand!

 Mar 28, 2021

59 Online Users

avatar
avatar