Pasimplehin ( 8 + 9)?

Sagot:

#sqrt (sqrt8 + sqrt9) = 1 + sqrt2 #

Paliwanag:

Hayaan #sqrt (sqrt8 + sqrt9) = sqrta + sqrtb #

Squaring # sqrt8 + sqrt9 = a + b + 2sqrt (ab) # at bilang # sqrt9 = 3 #, meron kami # a + b + 2sqrt (ab) = 3 + sqrt8 = 3 + 2sqrt2 #

Kaya nga # a + b = 3 # at # ab = 2 #

i.e. # a = 3-b # at kaya # (3-b) b = 2 # o # 3b-b ^ 2 = 2 #

o # b ^ 2-3b + 2 = 0 # i.e. # (b-2) (b-1) = 0 #

samakatuwid # b = 1 # o #2#.

at pagkatapos # a = 2 #o # a = 1 #

Obserbahan na humantong sila sa parehong solusyon

Kaya nga #sqrt (sqrt8 + sqrt9) = sqrt1 + sqrt2 = 1 + sqrt2 #