Answer:
Algebraic: x = 5 / 2, - 5/2
Graphical: 2.50, - 2.50
Explanation:
First, we solve the equation algebraically.
[tex]16x^4=625[/tex]
dividing both sides by 16 gives
[tex]x^4=\frac{625}{16}[/tex]
Finally, taking the fourth root of both sides gives
[tex]\sqrt[4]{x^4}=\sqrt[4]{\frac{625}{16}}[/tex][tex]x=\sqrt[4]{\frac{625}{16}}[/tex][tex]x=\pm\frac{5}{2}[/tex]
which can be rewritten as
[tex]\boxed{x=-\frac{5}{2},\frac{5}{2}}[/tex]
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
