Če so korenine x ^ 2-4x + 1 alfa & beta, potem je alfa ^ beta * beta ^ alfa?

Odgovor:

# alfa ^ beta * beta ^ alpha ~ ~ 0,01 #

Pojasnilo:

Korenine so:

# x = (4 + -sqrt ((- 4) ^ 2-4)) / 2 #

# x = (4 + -sqrt (16-4)) / 2 #

# x = (4 + -sqrt12) / 2 #

# x = (4 + -2sqrt2) / 2 #

# x = 2 + sqrt3 ali 2-sqrt3 #

# alfa ^ beta * beta ^ alfa = (2 + sqrt3) ^ (2-sqrt3) * (2-sqrt3) ^ (2 + sqrt3) ~~ 0,01 #