Ratkaise q 38?

Vastaus:

Vastaus on #option (2) #

Selitys:

Identiteetti on

# (X + c) ^ 2 = x ^ 2 + 2cx + c ^ 2 #

Tässä, Yhtälö on

# (A ^ 2-3a + 2) x ^ 2 + (a ^ 2-4) x + (a ^ 2-a-2) = 0 #

# (A-2) (a-1) x ^ 2 + (a + 2) (a-2) x + (a-2) (a + 1) = 0 #

Jakaminen # (A-2) (a-1) #

# X ^ 2 + (a + 2) / (a-1) x + (a + 1) / (a-1) = 0 #

Siksi, # 2c = (a + 2) / (a-1) # ja # C ^ 2 = (a + 1) / (a-1) #

Poistaminen # C #

# 1/4 * (a + 2) ^ 2 / (a-1) ^ 2 = (a + 1) / (a-1) #

# (A + 2) ^ 2 = 4 (a + 1) (a-1) #

# ^ 2 + 4a + 4 = 4a ^ 2-4 #

# 3a ^ 2-4a-8 = 0 #

Syrjivä on

# Delta = b ^ 2-4ac = 16 + 96 = 112 #

Kuten #Delta> 0 #, on #2# todellisia ratkaisuja.

Vastaus on #option (2) #