How do you solve #|y^ { 2} - 84| = 5y#?

1 Answer
Jun 4, 2017

Answer:

See below.

Explanation:

#|y^ { 2} - 84| = 5y#

#y^ { 2} - 84 = 5y# and #y^ { 2} - 84 = -5y#

So, we set up two quadratics.

#y^ { 2} -5y- 84 =0#
#(y-12)(y+7)=0#
#y=12,-7#

#y^ { 2}+5y- 84 =0#
#(y+12)(y-7)=0#
#y=-12,7#

However, since the function is absolute, the right hand side cannot be negative. So, only positive values of #y# work, namely #12, 7#.