How do you solve #\root[ 4] { 8k + 12} - 9= - 11#?

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Answer 1 · 2017-04-11T22:56:51

This equation has no solutions.

Given:

#root(4)(8k+12)-9=-11#

Add #9# to both sides to get:

#root(4)(8k+12)=-2#

Note that #root(4)(...)# denotes the principal #4#th root which can not be negative, so this has no solutions.

Let us press on anyway to make sure:

Raise both sides of the equation to the #4#th power to get:

#8k+12 = 16#

Subtract #12# from both sides to get:

#8k = 4#

Divide both sides by #8# to find:

#k=1/2#

But we find:

#root(4)(8(color(blue)(1/2))+12) = root(4)(16) = 2 != -2#

So #k=1/2# is not a solution of the original equation.