Question

find the roots of the equation 1/x+1 +2/x+2=4/x+4=​

Answer 1

Step-by-step explanation:

that the given equation is not in the standard form of a quadratic equation.

Consider

x+1

1

+

x+2

2

=

x+4

4

That is,

x+1

1

=2[

x+4

2

−

x+2

1

]=2[

(x+4)(x+2)

2x+4−x−4

]

x+2

1

=2[

(x+2)(x+4)

x

]

x

2

+6x+8=2x

2

+2x

Thus, we have x

2

−4x−8=0, which is a quadratic equation.

(The above equation can also be obtained by taking LCM )

Using the quadratic formula we get,

x=

2(1)

4±

16−4(1)(−8)

=

2

4±

48

Thus, x=2+2

3

or 2−2

3

Hence, the solution set is {2−2

3

,2+2

3

}