SOLUTION: Solve the equation by making an appropriate substitution. 2x^1/2-5x^1/4-3=0

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Question 1058943: Solve the equation by making an appropriate substitution.
2x^1/2-5x^1/4-3=0
Answer by ikleyn(52756) About Me  (Show Source):
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Solve the equation by making an appropriate substitution.
2x^1/2-5x^1/4-3=0
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The appropriate substitution is

u = x^(1/4),

after which the equation takes the form

2u%5E2+-+5u+-+3 = 0.

u%5B1%2C2%5D = %285+%2B-+sqrt%285%5E2+%2B4%2A2%2A3%29%29%2F%282%2A2%29 = %285+%2B-+7%29%2F4.

Only positive root is allowed, which is u = 3.

Then x^(1/4) = 3  --->  x = 3%5E4 = 81.

Answer.  The solution is  x = 81.