Question

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

Answer 1

Answer:

$x = \frac{3}{2}orx=-\frac{3}{2}$

Step-by-step 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

$x=\frac{3}{2}$

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

$x=\frac{-3}{2}$

so $x=\frac{3}{2}$ and $x=\frac{-3}{2}$