Question

x-1/x=3 find solution by quadratic formula method​

Answer 1

Answer:

x = (-3 ± √13)/2

Note:

★ The possible values of the variable which satisfy the equation are called its roots or solutions .

★ A quadratic equation can have atmost two roots .

★ The discriminant of the quadratic equation ax² + bx + c = 0 is given as ; D = b² - 4ac and the solution (roots) is given as ; x = (- b ± √D)/2a .

Solution:

Here,

The given equation is ;

x - 1/x = 3

The given equation can be rewritten as ;

=> x - 1/x = 3

=> (x² - 1)/x = 3

=> x² - 1 = 3x

=> x² - 3x - 1 = 0

Now,

Comparing the above equation with the general form of quadratic equation ax² + bx + c = 0 ,

We have ;

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

Now,

=> Discriminant , D = b² - 4ac

=> D = (-3)² - 4•1•(-1)

=> D = 9 + 4

=> D = 13

Now,

The roots of the equation will be ;

=> x = (-b ± √D)/2a

=> x = [-(-3) ± √13] / 2×1

=> x = (-3 ± √13)/2

Hence,

x = (-3 ± √13)/2