If $23=x^4+\frac{1}{x^4}$, then what is the value of $x^2+\frac{1}{x^2}$?

Step-by-step explanation:

is given.

We want to find .

If we square the value we want to find, we should wind up with some terms of the left hand side of the given.

Expand:

(We used the identity: for expansion).

Simplify this value:

We are given that the sum of the first two terms is 23.

This means .

Let's simplify the right hand side.

Now to find the value we want we must simply take the square root of both sides.

Simplify the right hand side:

Since is positive for any real value (that is not zero), then we can conclude .

use an equation of ratios to determine the amount of gas needed to fill the tank.

    0.2             0.8

  =    

288.75             x

                                                              231 gal

so, 0.2x = (0.8)(288.75 gal), and x = = 1155 gal.

                                                                0.2

it would take 1155 gal. to fill the tank.

the cost would be

1155 gal         $3

* = $3465   (answer)

      1           1 gal

hope this you

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step-by-step explanation: