How do you evaluate #(y - \frac { 2} { 3} ) ^ { 2} = \frac { 8} { 9}#?

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Answer 1 · 2017-12-28T19:54:04

Use the square root on both sides. (remember that the right side is #+-)#
Add #2/3# to both sides
Separate into two equations:

Use the square root on both sides:

#y -2/3 = +-sqrt(8/9)#

Add #2/3# to both sides:

#y =2/3 +-sqrt(8/9)#

The radical contains a #4/9# as a factor:

#y =2/3 +-2/3sqrt2#

Separate into two equations:

#y = 2/3(1-sqrt2)# and #y = 2/3(1+sqrt2)#