Question

V^2+2=8-4v^2 solve the question algebically

Answer 1

Answer:

v =  ± sqrt(6/5)

Step-by-step explanation:

v^2+2=8-4v^2

Add 4v^2 to each side

v^2+ 4v^2+2=8-4v^2+ 4v^2

5v^2 +2 = 8

Subtract 2 from each side

5v^2  +2-2 = 8-2

5 v^2 = 6

Divide each side by 5

5v^2 /5 = 6/5

v^2 = 6/5

Take the square root of each side

sqrt(v^2)  = ± sqrt(6/5)

v =  ± sqrt(6/5)

Answer 2

Answer:

$v=\sqrt{\frac{6}{5} }$,$-\sqrt{\frac{6}{5} }$

Step-by-step explanation:

Start with:

$v^2+2=8-4v^2$

Add $4v^2$ to both sides of the equation.

$4v^2+v^2+2=8$

Combine like terms.

$5v^2+2=8$

Subtract $2$ from both sides of the equation.

$5v^2=8-2$

Combine like terms.

$5v^2=6$

Divide both sides of the equation by the coefficient of $v^2$, which is $5$.

$v^2=\frac{6}{5}$

Square root $v^2$ and $\frac{6}{5}$.

$\sqrt{v^2} =\sqrt{\frac{6}{5} }$

Solve.

$v=\sqrt{\frac{6}{5} }$,$-\sqrt{\frac{6}{5} }$