11. Solve the following equation for real 𝑦 :
2 !$2𝑦 − 1 = 𝑦 ! + 1
1
!
!
!
12. √25 + √5 + 1
!
= 𝐴 √25 + 𝐵 √5 + 𝐶
𝐴 + 𝐵 + 𝐶 =?
3! = 6
3"!#$ = ?
13.
14. 2(√2𝑠 − 16 − √𝑠) − 8 = 0
Solve for s
15. Let 𝑥 be a real number satisfying the equation 𝑥 " − 3𝑥 + 1 = 0. Then 𝑥#$ − 𝑘𝑥 % + 1 = 0 for some constant 𝑘.
Compute 𝑘.
16. Find 𝑖 "&""
𝑎√𝑎 + 𝑏√𝑏 = 183
𝑏√𝑎 + 𝑎√𝑏 = 182
17.
'
𝑎, 𝑏 ∈ ℝ
!
!
(
(𝑎 + 𝑏) =?
!
18. √𝑥 + √𝑥 − 16 = √𝑥 − 8
Solve for x
19. Solve for real values of 𝑥 :
#
#
1 "
1 "
?𝑥 − @ + ?1 − @ = 𝑥
𝑥
𝑥
20.
𝑥 " = 17𝑥 + 𝑦
𝑦 " = 𝑥 + 17𝑦
𝑥≠𝑦
$𝑥 " + 𝑦 " + 1 =?
21. Solve for all real numbers 𝑥 for which:
(𝑥 " − 7𝑥 + 11))
" *#!)+,"
=1