Odgovor:
#sqrt (sqrt8 + sqrt9) = 1 + sqrt2 #
Pojasnilo:
Let #sqrt (sqrt8 + sqrt9) = sqrta + sqrtb #
Kvadriranje # sqrt8 + sqrt9 = a + b + 2sqrt (ab) # in kot # sqrt9 = 3 #, imamo # a + b + 2sqrt (ab) = 3 + sqrt8 = 3 + 2sqrt2 #
Zato # a + b = 3 # in # ab = 2 #
t.j. # a = 3-b # in zato # (3-b) b = 2 # ali # 3b-b ^ 2 = 2 #
ali # b ^ 2-3b + 2 = 0 # t.j. # (b-2) (b-1) = 0 #
zato # b = 1 # ali #2#.
in potem # a = 2 #ali # a = 1 #
Opazujte, da vodijo do enake rešitve
Zato #sqrt (sqrt8 + sqrt9) = sqrt1 + sqrt2 = 1 + sqrt2 #
