Answer :
Answer: x=-2
Step-by-step explanation: Eliminate the fractional exponent by raising both sides of the equation by the reciprocal of the exponent.
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Answer:
x = -2.
Step-by-step explanation:
(x + 5)^1/2 = (5 - 2x)^1/4
Taking both sides to the power of 4:
(x + 5)^2 = 5 - 2x
x^2 + 10x + 25 = 5 - 2x
x^2 + 12x + 20 = 0
(x + 10(x + 2) = 0
x = -2, -10
Test for extraneous roots.
When x = -10
(-10 + 5)^1/2 = (-5)^1/2 which is not real.
When x = -2
(-2+5)^1/2 = 3 ^1/2
(5 - 2*(-2)) ^1/4 = 9 ^ 1/4 = 3^1/2
so x = -2 is a root.