Question

ASAP 100 POINTS

ENTER THE VALUE OF X. PHOTO attached

Answer 1

x = 3

Explanation:

given:

f(x) = g(x)

f(x) = x³ - 3x² + 2

g(x) = x² - 6x + 11

find: the value of x

solution:

• as given f(x) = g(x)

• equate each side x³ - 3x² + 2 = x² - 6x + 11
• combine similar terms and equate to zero: x³ - 4x² + 6x - 9 = 0
• solve by factoring: (x - 3) (x² - x + 3)
• use the Zero factor principle: x - 3 = 0
• x = 3
• for x² - x + 3 = 0 ----this is a complex solution.

therefore, the value of x = 3

Answer 2

x=3

Explanation:

f(x) = x^3 -3x^2 +2

g(x) = x^2 -6x +11

Set them equal to each other

x^3 -3x^2 +2 = x^2 -6x +11

Subtract x^2 from each side

x^3 -3x^2 +2 = x^2 -6x +11

x^3 -3x^2-x^2 +2 = x^2-x^2 -6x +11

x^3 -4x^2 +2 = -6x +11

Add 6x to each side

x^3 -4x^2+6x +2 = -6x+6x +11

x^3 -4x^2+6x +2 = 11

Subtract 11

x^3 -4x^2+6x +2-11 = 11-11

x^3 -4x^2+6x -9 = 0

Factor

(x-3)(x^2-x+3)=0

Using the zero product property

x-3 =0 x^2 -x+3 =0

x=3 x^2 -x+3 =0

This will give a complex solution