Source: algebrica.org - CC BY-NC 4.0 https://algebrica.org/exercises/irrational-equation-a-4/ Fetched from algebrica.org test 14697; source modified 2025-04-25T17:07:54.
Before you begin, review the key concepts behind irrational equations to better follow the solution process.
Solve the irrational equation
\sqrt{3x^2-8x} = -5
The solution is immediate and requires no computation. The equation is of the form:
\sqrt[n]{f(x)} = k
where $k$ is a negative real number and $n$ is even. Since even-indexed roots of real numbers are always non-negative, the equation has no real solution.
Solution
\not \exists\; x \in \mathbb{R}