Question

((b^n)^2)/((b^n)*(b^n+2)) Write as a power of b.
((1)-(y^-1))/((y)-(y^-1)) Simplify.
(2^x) + (2^-x) = (5/2) Solve for x. ((b^n)^2)/((b^n)*(b^n+2)) Write as a power of b.
((1)-(y^-1))/((y)-(y^-1)) Simplify.
(2^x) + (2^-x) = (5/2) Solve for x. @Mathematics

Answer 1

((b^n)^2)/((b^n)*(b^n+2))
\[ = \frac{(b^n)^2}{b^n.b^{n+2}} = \frac{b^{2n}}{b^{2n+2}} = b^{2n}.b^{-(2n+2)} = b^{2n - 2n - 2} = b^{-2} \]

Answer 2

= 1/b^2

Answer 3

For the second equation, multiply top and bottom by y

Answer 4

For the third equation: (2^x) + (2^-x) = (5/2)
1. Multiply both sides by 2^x
2. Set u = 2^x
3. Turn the resulting equation from step 1 into a quadratic equation in u
4. Solve that equation for u
5. Now set u back equal to 2^x and solve for x.

Answer 5

...for second equation, after multiplying top and bottom by y, then factorize and simplify.

Answer 6

what's y times (1-(y^-1))
and what's y times (y-(y^-1))

Answer 7

\[ y(1-y^{-1}) = y(1 - 1/y) = y - (y/y) = y - 1\]
You figure out the other one.

Answer 8

after I find both, then what?

Answer 9

nvm I got it

Answer 10

how about last one

Answer 11

Look at what you've got and see if you can simplify further, which you should be able to.

For the last one, I wrote down the approach for you above in steps.

Answer 12

I don't get how u do it

Answer 13

For the third equation: (2^x) + (2^-x) = (5/2)
1. Multiply both sides by 2^x
2. Set u = 2^x
3. Turn the resulting equation from step 1 into a quadratic equation in u
4. Solve that equation for u
5. Now set u back equal to 2^x and solve for x.

======
1. Multiply both sides by 2^x

\[ (2^x)^2 + 2^{-x}.2^x = 5/2 . 2^x \]
\[ (2^x)^2 + 1 = 5/2 . 2^x \]

2. Set u = 2^x

\[ u^2 + 1 = 5/2 . u \]

3. Turn the resulting equation from step 1 into a quadratic equation in u

\[ u^2 - (5/2)u + 1 = 0 \]

You take it from here.

Answer 14

got it thanks

Answer 15

what's the period mean?

Answer 16

after the 2s?

Answer 17

multiplication

Answer 18

I can't factor it :(

Answer 19

and btw, the answers are -1 and 1, but idk how