Question

Solve the radical equation 3x2−10−−−−−−√5+7=4
to find the two solutions.(1 point)
x=

Answer 1

To solve the equation, we need to isolate the radical term on one side of the equation.

Starting with the given equation:

3√(5x^2 - 10) + 7 = 4

Subtracting 7 from both sides:

3√(5x^2 - 10) = -3

Dividing both sides by 3:

√(5x^2 - 10) = -1

To eliminate the square root, we need to square both sides of the equation:

(√(5x^2 - 10))^2 = (-1)^2

5x^2 - 10 = 1

Adding 10 to both sides:

5x^2 = 11

Dividing both sides by 5:

x^2 = 11/5

Taking the square root of both sides:

x = ±√(11/5)

So, the two solutions are:

x = √(11/5)

x = -√(11/5)