Question

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

Answer 1

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

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