1) find all the values of x, ( 2/ x-3) ² -3(2/ x-3)-4=0
2) Find all the values of x, ( √2x + 2) - (√x + 2 ) = 1
3) Find all the values of x, log₄x = - 3/2
2) Find all the values of x, ( √2x + 2) - (√x + 2 ) = 1
3) Find all the values of x, log₄x = - 3/2
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(1) (2 / x - 3)² -3(2 / x - 3) - 4 = 0
4/(x - 3)² - 6(x - 3) / (x - 3)² = 4
22 - 6x/(x - 3)² = 4
22 - 6x = 4(x - 3)²
22 - 6x = 4x² - 24x + 36
4x² - 18x + 14 = 0
(4x - 14)(x - 1) = 0
x = 7/2 or 1.
(2) (√2x + 2) - (√x + 2) = 1
√2x - √x = 1
2x² - x = 1
2x² - x - 1 = 0
(2x + 1)(x - 1) = 0
x = -1/2 or 1
(3) log_4(x) = -3/2
x = 4^(-3/2) = 1/8
4/(x - 3)² - 6(x - 3) / (x - 3)² = 4
22 - 6x/(x - 3)² = 4
22 - 6x = 4(x - 3)²
22 - 6x = 4x² - 24x + 36
4x² - 18x + 14 = 0
(4x - 14)(x - 1) = 0
x = 7/2 or 1.
(2) (√2x + 2) - (√x + 2) = 1
√2x - √x = 1
2x² - x = 1
2x² - x - 1 = 0
(2x + 1)(x - 1) = 0
x = -1/2 or 1
(3) log_4(x) = -3/2
x = 4^(-3/2) = 1/8