Ako zjednodušíte sqrt (x-1) + sqrt (2x) = 3?

odpoveď:

# Rarrx = 2 #

vysvetlenie:

#rarrsqrt (x-1) + sqrt (2x) = 3 #

#rarrsqrt (x-1) = 3-sqrt (2x) #

#rarr sqrt (x-1) ^ 2 = 3-sqrt (2x) ^ 2 #

# Rarrx-1 = 9-6sqrt (2x) + 2x #

# Rarr6sqrt (2x) = x + 10 #

#rarr 6sqrt (2x) ^ 2 = x + 10 ^ 2 #

# Rarr36 * (2 x) = x ^ 2 + 20x + 100 #

# Rarrx ^ 2-52x + 100 = 0 #

# Rarrx ^ 2-2 * x * 26 + 26 ^ 2-26 ^ 2 + 100 = 0 #

#rarr (x-26) ^ 2 = 26 ^ 2-100 = 576 #

# Rarrx-26 = sqrt (576) = + - 24 #

# rarrx = 26 + 24,26-24 = 50 alebo 2 #

uvedenie # X = 50 # v danej rovnici dostaneme, #rarrsqrt (50-1) + sqrt (2 * 50) = 17 (zamietnutý) #

uvedenie # X = 2 # v danej rovnici dostaneme, #rarrsqrt (2-1) + sqrt (2 * 2) = 3 (prijatý) #

Takže požadovaná hodnota x je #2.#