If f (x) = x2 – 3x + 4, then find the values of x satisfying the equation f (x) = f (2x + 1).

Asked by Sakshi | 1 year ago |  59

##### Solution :-

Given:

f(x) = x2 – 3x + 4.

Let us find x satisfying f (x) = f (2x + 1).

We have,

f (2x + 1) = (2x + 1)2 – 3(2x + 1) + 4

= (2x) 2 + 2(2x) (1) + 12 – 6x – 3 + 4

= 4x2 + 4x + 1 – 6x + 1

= 4x2 – 2x + 2

Now, f (x) = f (2x + 1)

x2 – 3x + 4 = 4x2 – 2x + 2

4x2 – 2x + 2 – x2 + 3x – 4 = 0

3x2 + x – 2 = 0

3x2 + 3x – 2x – 2 = 0

3x(x + 1) – 2(x + 1) = 0

(x + 1)(3x – 2) = 0

x + 1 = 0 or 3x – 2 = 0

x = –1 or 3x = 2

x = –1 or $$\dfrac{2}{3}$$

The values of x are –1 and $$\dfrac{2}{3}$$

Answered by Sakshi | 1 year ago

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