1) 2x = 1-x√3
x(2+√3) = 1
x = 1/(2+√3)
1*(2-√3) 2-√3
x= --------------------- = ---------- = 2 - √3
(2+√3)(2-√3) 4 - 3
3) x√5 + 3 = x√3 +5
x(√5 - √3) = 5 - 3
2 2(√5 +√3)
x= --------- = -------------- = √5 - √3
√5 -√3 5-3
2) x√5 - 12 = x
x(√5-1) = 12
12(√5 + 1) 12(√5 - 1)
x= ------------------ = --------------- = 3(√5 - 1)
(√5 - 1)(√5+1) 5 - 1
4) 2x√6 - √3 = 2√6 +x√3
x(2√6-√3) =2√6+√3
2√6+√3 (2√6+√3)² 24 +4√18 +3 27+12√2 9+4√2
x=------------ =---------------- = -------------------- = ------------- = ---------
2√6 -√3 4*6 -3 21 21 7