Rešite naslednji sistem enačbe: [((1), sqrt (2) x + sqrt (3) y = 0), ((2), x + y = sqrt (3) -sqrt (2))]?

Odgovor:

# {(x = (3sqrt (2) -2sqrt (3)) / (sqrt (6) -2)), (y = (sqrt (6) -2) / (sqrt (2) -sqrt (3))):} #

Pojasnilo:

Od #(1)# imamo

#sqrt (2) x + sqrt (3) y = 0 #

Razdelitev obeh strani z #sqrt (2) # nam daje

#x + sqrt (3) / sqrt (2) y = 0 "(*)" #

Če odštejemo #'(*)'# od #(2)# dobimo

# x + y- (x + sqrt (3) / sqrt (2) y) = sqrt (3) -sqrt (2) - 0 #

# => (1-sqrt (3) / sqrt (2)) y = sqrt (3) -sqrt (2) #

# => y = (sqrt (3) -sqrt (2)) / (1-sqrt (3) / sqrt (2)) = (sqrt (6) -2) / (sqrt (2) -sqrt (3))) #

Če nadomestimo vrednost, za katero smo našli # y # nazaj v #'(*)'# dobimo

#x + sqrt (3) / sqrt (2) * (sqrt (6) -2) / (sqrt (2) -sqrt (3)) = 0 #

# => x + (3sqrt (2) -2sqrt (3)) / (2-sqrt (6)) = 0 #

# => x = - (3sqrt (2) -2sqrt (3)) / (2-sqrt (6)) = (3sqrt (2) -2sqrt (3)) / (sqrt (6) -2) #

Tako pridemo do rešitve

# {(x = (3sqrt (2) -2sqrt (3)) / (sqrt (6) -2)), (y = (sqrt (6) -2) / (sqrt (2) -sqrt (3))):} #