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

Solve this equation. leave the answer as an improper

bella4269

10.03.2022

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

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

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