currysauce
Actuary in the making
root((k+1)/2) - root((k-1)/2) = root (k - root(k^2-1))
-
Best of luck to the class of 2024 for their HSC exams. You got this! Let us know your thoughts on the HSC exams here -
YOU can help the next generation of students in the community! Share your trial papers and notes on our Notes & Resources page
Prove this identity (1 Viewer)
- Thread starter currysauce
- Start date
I
icycloud
Guest
Let LHS = Sqrt((k+1)/2) - Sqrt((k-1)/2)
LHS2 = (k+1)/2 + (k-1)/2 - 2Sqrt((k+1)(k-1)/4)
= k - Sqrt(k^2-1)
Thus, LHS = Sqrt(LHS2) = Sqrt(k-Sqrt(k^2-1)) = RHS
LHS2 = (k+1)/2 + (k-1)/2 - 2Sqrt((k+1)(k-1)/4)
= k - Sqrt(k^2-1)
Thus, LHS = Sqrt(LHS2) = Sqrt(k-Sqrt(k^2-1)) = RHS
NightShadow
Member
- Joined
- Nov 10, 2004
- Messages
- 79
- Gender
- Male
- HSC
- 2006
what about restrictions because you're square rooting? wont you have a negative answer component as well?
currysauce
Actuary in the making
thankyou
I
icycloud
Guest
Well, k >= 1 for LHS to be defined.
And LHS >= 0 for k >= 1.
Therefore, we take the positive root for RHS.
And LHS >= 0 for k >= 1.
Therefore, we take the positive root for RHS.