Thread: Simultaneous equations (tough one): 8^x 64^y = 128, sqrt[12y - 7] = x

1. Originally Posted by Denis
8^x * 64^y = 128 [1]

SQRT(12y - 7) = x [2]

By inspection of [1], easily seen that x=1/3 and y=1.
Other solution not easily seen?

Find it, by first solving for y: 18y^2 - 96y + 56 = 0

2. Originally Posted by Denis
8^x * 64^y = 128 [1]
SQRT(12y - 7) = x [2]

By inspection of [1], easily seen that x=1/3 and y=1.

Seems that [2] contains a typo(s)....
No ,mister, no typos

3. Rewrite Equation 1

2^(3x+6y) = 2^7

Then equation 1 becomes simply,
3x+6y = 7

4. Originally Posted by mmm4444bot
Other solution not easily seen?
According to 1st post, the OP apparently was learning
how to solve "2 unknowns, 2 equations" problems.

I showed one possible solution to his 1st equation.
This was mainly to see if the OP understood.

I made up a similar case:
x=3, y=2
2^x * 5^y = 200 [1]
sqrt(12y - 15) = x [2]

Then used Wolfram (to "see"):
http://www.wolframalpha.com/input/?i...t(12*y-15)%3Dx

So no problems with a "proper" set of 2 equations.

I then tried the OP's 2 equations:
http://www.wolframalpha.com/input/?i...rt(12*y-7)%3Dx

So I assumed there was something wrong
with the equations...

My apologies...

5. Originally Posted by Denis
I showed one possible solution to his 1st equation.
This was mainly to see if the OP understood.
Did you see their work?

When I tried it, Wolfram showed the solution graphically. If you want to enlarge the graph or see further computations, ya gotta pay.

6. Originally Posted by Bob Brown MSEE
2^(3x+6y) = 2^7

Then equation 1 becomes simply,
3x+6y = 7
6x+12y = 14 [1]
12y - 7 = xx [2]

so
6x+ (xx+7) = 14

x=1 or x=-7

trying in [1], x=1
Answ: x=1, y=2/3

Wolfram Solution

7. Originally Posted by Bob Brown MSEE
6x+12y = 14 [1]
12y - 7 = xx [2]

so
6x+ (xx+7) = 14
I like it.

8. Originally Posted by Tuharramah
Sqrt (12y-7)=x
8^x * 64^y=128

So 2^3x + 2^6y = 2^7

3*sqrt (12y-7) +6y =7
I wouldn't go this way. Instead:

. . . . .3x + 6y = 7

. . . . .12y - 7 = x^2

Multiply the first equation by -2:

. . . . .-6x - 12y = -14

. . . . .12y - 7 = x^2

. . . . .-6x - 7 = x^2 - 14

. . . . .0 = x^2 + 6x - 7

. . . . .0 = (x + 7)(x - 1)

...and so forth.

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