Question

(x-68)^(2/5) = 81. There are apparently multiple answers, and I've only found one (59117.) Please help!

Answer 1

Hello there.

Answer 2

Any ideas?

Answer 3

-59117?

Answer 4

Afraid I've already tried that one. I guess I'll give it one more try just for luck.

Answer 5

well maybe not - it is a fractional root

Answer 6

Nope nope nope.

Answer 7

Yeah, I've no idea how I'm supposed to find the second answer.

Answer 8

Give up? lol

Answer 9

haha

Answer 10

Well...I guess I'll just ask my bf when he comes online. Thank you though!

Answer 11

okay, i found a way to graph it online and it doesn't seem like there would be another answer

Answer 12

Doesn't surprise me. I really should've just gone to a tutoring session.

Answer 13

yeah, that can help

Answer 14

Anyway...not to be clingly/overly demanding...but...care to help me with another problem?

Answer 15

Namely this: x^{3/8} - 12 x^{3/16} + 36 = 0

Answer 16

clingy? it's math! not a problem, um... that's... a problem :-P

Answer 17

I mean...I'm presumably supposed to use substitution.

Answer 18

So say I replace x^(3/8) with y.

Answer 19

u - 12u^(1/2) + 36?

Answer 20

That gives me y - 12y^2 + 36, which is alot less intimidating

Answer 21

yep

Answer 22

Or wait...no. Is it 12y^(1/2)?

Answer 23

y ^2 would back substitute to x ^(3/4)

Answer 24

Oh...maybe that's why then...

Answer 25

Wait...but 3/16 * 2 = 3/8.

Answer 26

not if you replace y = x ^(3/8)

Answer 27

But that wouldn't make sense. Because the object is to substitute another value in for the variable/exponent combination in the middle (i.e. 12x^3/16)

Answer 28

x^{3/8} - 12 x^{3/16} + 36 = 0

would go to:
y - 12y^2 + 36 = 0

Answer 29

But 3/8 * 2 doesn't equal 3/16

Answer 30

oops!
y - 12y^(1/2) + 36 = 0

Answer 31

Yeah, but it'd still make more sense to just substitute y^2 for x^(3/8)

Answer 32

ha!

Answer 33

but then where does substitution come in?