How do you solve 3y^2-12=03y212=0?

3 Answers
Mar 13, 2018

y = +- 2y=±2

Explanation:

It is necessary to manipulate the equation so that the unknown variable (here, yy) is on its own on the left hand side of the equation. It will be equal to whatever is on the right hand side of the equation.

To make a start, by inspection, it will be necessary to divide 3 y^23y2 by 33 to remove the coefficient (and leave just y^2y2). It is necessary to do the same thing to both sides of the equation, so every term must be divided by 33.

That is,

3y^2 - 12 = 03y212=0

implies

(3y^2)/3 - 12/3 = 0/33y23123=03

that is

y^2 - 4 = 0y24=0

This may be rearranged (by adding 44 to both sides of the equation) to yield

y^2 = 4 y2=4

To retrieve yy on its own, it is necessary to take the square root of both sides. As 44 is a perfect square, this will be easy but take care! Remember that square numbers have two roots, a positive one and a negative one.

So,

y^2 = 4 y2=4

implies

sqrt(y^2) = sqrt(4) y2=4

that is

y = 2y=2
or
y = -2y=2

Mar 13, 2018

y = +-2y=±2

Explanation:

3y^2-12=03y212=0

Multiply 3 xx (-12)3×(12) to get -3636 and use that to find two factors that when multiplied give -3636 and when added give 00

3y^2+6y-6y-12=03y2+6y6y12=0

3y(y+2)-6(y+2)=03y(y+2)6(y+2)=0

Pull out the factors of the equation 3y^2-12=03y212=0

(3y-6) (y+2) = 0(3y6)(y+2)=0

So

3y-6=0 => y+2=03y6=0y+2=0

3y=6 => y=-23y=6y=2

Mar 13, 2018

y = +-2y=±2

Explanation:

This is a Difference of Two Squares problem -- with a slight disguise because it is multiplied by 33

The Difference of Two Squares is a case of Special Factoring.

By memorization, the Difference of Two Squares factors like this:

a^2 - b^2=(a + b)(a - b)a2b2=(a+b)(ab)

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Given   3y^2−12=03y212=0    Solve for yy

1) Factor out the 3 to see the perfect squares
3 (y^2 - 4) = 0

2) Factor the Difference of the Two Squares
3 (y+2)(y-2)= 0

3) Set the factors equal to zero and solve for y

3= 0 larr discarded solution

y + 2 = 0
y = -2 larr one answer

y - 2 = 0
y = 2 larr the other answer

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Here's a video you can watch to see more about Special Factoring