Com es resol 5x = sqrt {74x + 3}?

Resposta:

# x = -1 / 25 color (blanc) ("xxx") orcolor (blanc) ("xxx") x = 3 #

Explicació:

Si # 5x = sqrt (74x + 3) #

llavors

(després de quadrar els dos costats)

#color (blanc) ("XXX") 25x ^ 2 = 74x + 3 #

(restant # 74x + 3 # dels dos costats)

#color (blanc) ("XXX") 25x ^ 2-74x-3 = 0 #

(factoring)

#color (blanc) ("XXX") (25x + 1) (x-3) = 0

(deixant dues possibilitats)

#color (blanc) ("XXX") {: (25x + 1 = 0, color (blanc) ("xx") orcolor (blanc) ("xx"), x-3 = 0), (rarr x = - 1/25,, rarrx = 3):}

Resposta:

#x = -1/25, 3 #

Explicació:

# 5x = sqrt (74x + 3) #

# (5x) ^ 2 = 74x + 3 #

# 25x ^ 2 = 74x + 3 #

# 25x ^ 2 - 74x - 3 = 0 #

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

#x = (74 + - sqrt (-74 ^ 2 + 300)) / 50 #

#x = (74 + - 76) / 50 #

#x = -1/25, 3 #