Question

Solve this equation.
Leave the answer as an improper fraction.
3x^2 + 2 = 11 - x^2

Answer 1

`x = (3)/(2)orx=-(3)/(2)`

Explanation:

The given Equation is

`3x^(2) + 2 = 11-x^(2)` .................(i)

Adding (
`x^(2) -11` ) on both sides of (i)

`3x^(2)+2+x^(2)-11 = 11-x^(2)+x^(2)-11`

solving and cancelling out the terms will give

⇒
`4x^(2) -9=0`

⇒
`(2x)^(2) -(3)^(2) = 0` ...................(ii)

Now we Know that

`(a)^(2) -(b)^(2) = (a-b)(a+b)`

Applying this on equation (ii)

`(2x-3)(2x+3)=0`

This will lead us to

Either 2x-3 =0 .......(iii) or 2x+3=0 ..........(iv)

Solving equation (iii) for value of x

2x - 3 =0

adding 3 on both sides

2x -3 +3 = 0+ 3

2x = 3

Cross multiplying gives

`x=(3)/(2)`

Solving equation (iv) for value of x

2x + 3 =0

adding -3 on both sides

2x -3 +3 = 0- 3

2x = -3

Cross multiplying gives

`x=(-3)/(2)`

so
`x=(3)/(2)` and
`x=(-3)/(2)`