No.1 | 4 * sqrt(4*x + 1)=3 * sqrt(7*x + 2) |
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One root on a side of the
equation leads to a linear equation. |
No.2 | sqrt(x + 1) + sqrt(4*x + 4)=sqrt(9*x + 9) |
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Two roots on one side of the
equation usually leads to a equation of degree two. However, this
particular equation turns out to hold for any x. |
No.3 | sqrt(4*x + 1) - sqrt(x + 3) = sqrt(x - 2) |
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This equation reduces to a
linear equation, luckly. |
No.4 | sqrt(x + 12) + sqrt(x - 3) = sqrt(x + 32)
- sqrt(5 + x) |
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This equation is calculated
correcty, but finally fails due to the lack of a canonical simplifier
for formulae with roots -- thus a nice todo. |
No.5 | sqrt(29 - sqrt(x^2 - 9)) = 5 |
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This equation has two solutions. |
No.6 | 2*sqrt(261 - x) - sqrt(2 + 2*x) =
sqrt(2)*sqrt(5 - 3*x) |
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There is something wrong ---
but you can trace, how it goes wrong ! |
No.7 | (2*x + 1) * x^2 = 0 |
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This one has three solutions,
as expected (one of them a 'double' solution). |
No.8 | b^2
* x^2 + a^2 * y^2 = a^2 * b^2 |
No.9 | (a/2)^2 + (b/2)^2 = r^2 , a = ? |
No.10 | 2*sqrt(r^2 - (u/2)^2) - u^2/(2*sqrt(r^2 -
(u/2)^2)) = 0 , u = ? |
No.11 | y^2
= 2*p*x , y = ? |