Question

find the number of real roots​

Answer 1

Answer:

Real solutions of x is

Real solutions of x is

x = (1 - √13)/2

x = (1 + √13)/2

x = (-1 + √141)/14

x = (-1 - √141)/14

Step-by-step explanation:

We have,

3x² - 4 |x² - 1| + x - 1 = 0

Now,

We know that,

| x² - 1 | = ± (x² - 1)

= (x² - 1) or (-x² + 1)

Now, solving the equation,

3x² - 4 |x² - 1| + x - 1 = 0

3x² - 4(x² - 1) + x - 1 = 0

OR

3x² - 4(-x² + 1) + x - 1 = 0

Then,

3x² - 4x² + 4 + x - 1 = 0

OR

3x² + 4x² - 4 + x - 1 = 0

-x² + x - 3 = 0

OR

7x² + x - 5 = 0

Using the Quadratic formula,

x = (-b ± √(b² - 4ac))/2a

Then,

-x² + x - 3 = 0

ax² + bx + c = 0

a = (-1), b = 1, c = (-3)

OR

7x² + x - 5 = 0

ax² + bx + c = 0

a = 7, b = 1, c = (-5)

So,

x = [-1 ± √1² + 4(-1)(-3)]/2(-1)

x = (-1)[-1 ± √1 + 12]/2

x = (-1)[-1 ± √13)/2

OR

x = [-1 ± √1² - 4(7)(-5)]/2(7)

x = [-1 ± √1 + 140]/14

x = [-1 ± √141]/14

Hence,

Real solutions of x is

x = (-1)[-1 + √13]/2

x = (1 - √13)/2

Also,

x = (-1)[-1 - √13]/2

x = (1 + √13)/2

And

x = (-1 + √141)/14

x = (-1 - √141)/14

Hope it helped you and believing you understood it...All the best