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

3 Answers
Mar 13, 2018

Answer:

#y = +- 2#

Explanation:

It is necessary to manipulate the equation so that the unknown variable (here, #y#) 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^2# by #3# to remove the coefficient (and leave just #y^2#). It is necessary to do the same thing to both sides of the equation, so every term must be divided by #3#.

That is,

#3y^2 - 12 = 0#

implies

#(3y^2)/3 - 12/3 = 0/3#

that is

#y^2 - 4 = 0#

This may be rearranged (by adding #4# to both sides of the equation) to yield

#y^2 = 4 #

To retrieve #y# on its own, it is necessary to take the square root of both sides. As #4# 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 #

implies

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

that is

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

Mar 13, 2018

Answer:

#y = +-2#

Explanation:

#3y^2-12=0#

Multiply #3 xx (-12)# to get #-36# and use that to find two factors that when multiplied give #-36# and when added give #0#

#3y^2+6y-6y-12=0#

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

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

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

So

#3y-6=0 => y+2=0#

#3y=6 => y=-2#

Mar 13, 2018

Answer:

# y = +-2#

Explanation:

This is a Difference of Two Squares problem -- with a slight disguise because it is multiplied by #3#

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)#

#color(white)(mmmmmmmm)#――――――――

Given   #3y^2−12=0#    Solve for #y#

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

#color(white)(mmmmmmmm)#――――――――

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