Question

Hello I need help on #5 I don’t know what I’m doing wrong, please help

Answer 1

Algebraic: x = 5 / 2, - 5/2

Graphical: 2.50, - 2.50

Step-by-step explanation:

First, we solve the equation algebraically.

`16x^4=625`

dividing both sides by 16 gives

`x^4=(625)/(16)`

Finally, taking the fourth root of both sides gives

`\sqrt[4]{x^4}=\sqrt[4]{(625)/(16)}`
`x=\sqrt[4]{(625)/(16)}`
`x=\pm(5)/(2)`

which can be rewritten as

`\boxed{x=-(5)/(2),(5)/(2)}`

Now we find the same solution using graphs.

We plot the equation and get:

From which we see that x = -2.5 and x = 2.5 are the solutions to the equation. But since we have to round to two decimal places, we write these solutions as x = -2.50, 2.50.

Note: The blue graph is y = 16x^4 and the blue line is y = 625.

To summerise:

Algebraic: x = 5 / 2, - 5/2

Graphical: 2.50, - 2.50