Question

\[\sqrt{x-4}-\sqrt[4]{x-4}=6\] why is the solution 85

Answer 1

please help and list each step, I am so confused

Answer 2

u have
\[\large \sqrt{x-4}-\sqrt[4]{x-4}=6 \]
which can be rewritten as
\[\large \sqrt{x-4}-\sqrt{\sqrt{x-4}}=6 \]

Answer 3

now let \(Y=\sqrt{x-4}\) so u have
\[\large Y-\sqrt{Y}=6 \]
or
\[\large Y-6=\sqrt{Y} \]
square both sides
\[\large Y^2-12Y+36=Y \]
or
\[\large Y^2-13Y+36=0 \]

Answer 4

I still don't understand?

Answer 5

this can be factored into (Y-4)(Y-9)=0

Answer 6

if Y=4 then \(\sqrt{x-4}=4\) gives you x=20

Answer 7

if Y=9 then \(\sqrt{x-4}=9\) gives you x=85

Answer 8

which part don't u understand? (sorry i'am having some problems posting things.)

Answer 9

oh i understand now!! I didn't realize the factoring