Find three solutions to the equation (x^2 - 9) (x^3 - 8) = 0.

The three roots of the equation are, x = + 9, x = - 9 and x = 2

Step-by-step explanation:

Data given in the question:

(x² - 9) (x³ - 8) = 0.

Now,

for the above relation to be true the following condition must be followed:

Either (x² - 9) = 0 ... (1)

or

(x³ - 8) = 0 ... (2)

Therefore,

considering the equation 1, we have

(x² - 9) = 0

adding 9 to the both sides

we get

x² - 9 + 9 = 0 + 9

or

x² + 0 = 9

taking the square root both the sides, we get

√x² = √9

or

x = ± 9

thus,

x = + 9 and, x = - 9

considering the equation 2, we have

(x³ - 8) = 0

adding 8 both the sides

we have

x³ - 8 + 8 = 0 + 8

or

x³ = 8

or

x³ = 2 * 2 * 2

taking the cube root both the sides, we get

∛x³ = ∛ (2 * 2 * 2)

or

x = 2

Hence,

The three roots of the equation are, x = + 9, x = - 9 and x = 2