olve the radical equation

Question

3
x
2
−
10
5
+
7
=
4
3
5

x
2
−10
​
+7=4 to find the two solutions. Separate your answers with a comma.

x
=
x=

Answer 1

To solve the equation

\[ 3\sqrt{x^2 - 10} + 7 = 4, \]

first, isolate the square root term. We do this by subtracting 7 from both sides:

\[ 3\sqrt{x^2 - 10} = 4 - 7, \] \[ 3\sqrt{x^2 - 10} = -3. \]

Next, divide both sides by 3:

\[ \sqrt{x^2 - 10} = -1. \]

Since the square root of a real number cannot be negative, there are no real solutions to this equation.

Thus, the result is:

\[ \text{No real solutions.} \]