Question

me ajudem a resolver essas equações irracionais por favorzinho!!!!

f)(⁴√x²+x)+4=2

g)x-3=2√x

h)2x=(9x)-2

i)(√x-3)=x-5

j)2(√x-1)=x-1

Answer 1

f)(⁴√x²+x)+4=2
(x^(2/4) + x) + 4 = 2
(x^(1/2) + x) = 2-4
√x + x = -2
√x = -2-x
x = (-2-x)^2
x = 4 + 2x + 2x + x^2
x^2 + 4x + 4 = x
x^2 + 3x + 4 = 0

(-3+-√9-4×4)/2
(-3+-√-7)/2

x' = (-3-√-7)/2
x" = (-3+√-7)/2

g)x-3=2√x
2√x = x-3 ×(^2)
(2√x)^2 = (x-3)^2
4x = x^2 - 6x + 9
x^2 - 10x + 9 = 0

(10+-√100-4×9)/2
(10+-√64)/2

x' = (10+8)/2 = 9
x" = (10-8)/2 = 1

h)2x=(9x)-2
2x-9x=-2
-7x=-2
x = -2/-7 = 2/7

i)(√x-3)=x-5
√x = x-5+3
x = (x-2)^2
x = x^2 - 4x + 4
x^2 - 5x + 4 = 0

(5+-√25-4×4)/2
(5+-√9)/2

x' = (5-3)/2 = 1
x" = (5+3)/2 = 4

j)2(√x-1)=x-1
2√x - 2 = x - 1
2√x = x - 1 + 2 ×(^2)
(2√x)^2 = (x+1)^2
4x = x^2 + 2x + 1
x^2 - 2x + 1 = 0

(2+-√4-4)/2
x = 2/2 = 1