If, x - 6/√x = 37
Then, find the value of x-6√x
let y = √x
we have y^2 - 6/y = 37; Find: y^2 - 6y
y^3 - 37y - 6 = 0
One root is y = -6
(which makes x=36 which does not solve the original equation)
Factor out the known root:
y^3 + 6y^2 - 6y^2 - 36y - y - 6 = 0
(y+6)(y^2 - 6y -1) = 0
other roots are (6 ± √40)/2 = 3 ± √10
y values: {-6, 3+√10, 3-√10}
x values: {36, 19+6√10, 19-6√10}
Plugging y values {-6, 3+√10, 3-√10} into y^2 - 6y
yields {72, 1, 1}, but the first is rejected since that y value does not solve the original equation.
Answer: 1
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Posted by Larry
on 2024-07-09 12:55:25 |
Solution
