Apakah sqrt (4x-3) = 2 + sqrt (2x-5)?

Jawapan:

# x = {3,7} #

Penjelasan:

Diberikan:

#sqrt (4x-3) = 2 + sqrt (2x-5) #

Kedua belah pihak:

#sqrt (4x-3) ^ 2 = (2 + sqrt (2x-5)) ^ 2 #

TETAPI mereka:

# 4x-3 = 4 + 4sqrt (2x-5) + 2x-5 #

Kumpulan seperti istilah:

# 2x-2 = 4sqrt (2x-5) #

Square kedua-dua belah LAGI:

# 4x ^ 2-8x + 4 = 16 (2x-5) #

Multiply:

# 4x ^ 2-8x + 4 = 32x-80 #

Kumpulan seperti istilah:

# 4x ^ 2-40x + 84 = 0 #

Faktor keluar #4#:

# 4 (x ^ 2-10x + 21) = 0 #

Kemudian

# 4 (x ^ 2 - 3x - 7x + 21) = 0 #

# 4 x (x-3) -7 (x-3) = 0 #

Jadi

# 4 (x-3) (x-7) = 0 #

Jawapan:

# x_1 = 3 # dan # x_2 = 7 #

Penjelasan:

#sqrt (4x-3) = 2 + sqrt (2x-5) #

#sqrt (4x-3) -sqrt (2x-5) = 2 #

# (sqrt (4x-3) -sqrt (2x-5)) ^ 2 = 2 ^ 2 #

# 4x-3 + 2x-5-2sqrt (8x ^ 2-26x + 15) = 4 #

# 6x-12 = 2sqrt (8x ^ 2-26x + 15) #

# 3x-6 = sqrt (8x ^ 2-26x + 15) #

# (3x-6) ^ 2 = 8x ^ 2-26x + 15 #

# 9x ^ 2-36x + 36 = 8x ^ 2-26x + 15 #

# x ^ 2-10x + 21 = 0 #

# (x-3) * (x-7) = 0 #

Oleh itu # x_1 = 3 # dan # x_2 = 7 #