Question

if f(x) = x2 - 3x + 2 and f(x) = f(x - 1) then find the value of x. ​

Answer 1

Answer:

X = 2 and X = 3

Step-by-step explanation:

f(x) = $x^{2}$ - 3x + 2   and f(x - 1)

Replace X in $x^{2}$ - 3x + 2 with (x - 1)

= $(x-1)^{2}$ - 3(x - 1) + 2

Expand the bracket.

$(x-1)^{2}$ = $x^{2}$ - 2x +1

3(x - 1) = 3x - 3

Therefore,

= $x^{2}$ - 2x +1 - (3x - 3) + 2

Expand the bracket

=  $x^{2}$ - 2x +1 - 3x + 3 + 2

Collect the like terms

= $x^{2}$  - 2x - 3x + 3 + 2 + 1

= $x^{2}$ - 5x + 6

Factorize this new equation

The LCM is 2 and 3        

= $x^{2}$ - 2x - 3x + 6

Group the equation

= ($x^{2}$ - 2x) - (3x + 6)

= x(x - 2) - 3(x - 2)

= (x - 2) (x - 3)

Therefore;

(x - 2) = 0; x = 2

(x - 3) = 0; x = 3

Then the final answer is;

X = 2 and X = 3

NOTE: Don't take the LCM as the answer, they are not always the right answer

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