Selesaikan x: y = sqrt ((4x + 1) / (3x-3))?

Jawapan:

# x = (1 + 3y ^ 2) / (3y ^ 2-4) #

Penjelasan:

# "ambil perhatian bahawa" sqrtaxxsqrta = (sqrta) ^ 2 = a #

# y = sqrt ((4x + 1) / (3x-3)) #

#color (biru) "menjaringkan kedua-dua belah" #

# y ^ 2 = (sqrt ((4x + 1) / (3x-3))) ^ 2 #

# rArry ^ 2 = (4x + 1) / (3x-3) #

# rArry ^ 2 (3x-3) = 4x + 1larrcolor (biru) "cross-multiplying" #

# rArr3xy ^ 2-3y ^ 2 = 4x + 1 #

# rArr3xy ^ 2-4x = 1 + 3y ^ 2larrcolor (biru) "mengumpul istilah dalam x" #

#rArrx (3y ^ 2-4) = 1 + 3y ^ 2larrcolor (blue) "factorising" #

# rArrx = (1 + 3y ^ 2) / (3y ^ 2-4) hingga (y! = + - 4/3) #

#color (biru) "Sebagai cek" #

# "mari x = 2" #

# "maka" y = sqrt (9/3) = sqrt3 #

# "ganti ke dalam ungkapan untuk x kita harus mendapat 2" #

# x = (1 + 3 (sqrt3) ^ 2) / (3 (sqrt (3) ^ 2-4)) = (1 + 9) / (9-4) = 10 /