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Find the solutions to x⁴-64=0 and the x-intercepts of the graph of y=x⁴-64.

User RoiHatam
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1 Answer

7 votes

Answer:

1.
x_1=2√(2)\\x_2=-2√(2)\\x_3=i2√(2)\\x_4=-i2√(2)

2.
A=(2√(2),0) and
B=(-2√(2),0)

Explanation:

We have the expression
x^4-64=0 to find the solutions we have to clear
x. Then,


x^4-64=0 Add 64 in both sides of the equation.


x^4-64+64=64\\x^4=64

Now we have to re-write the equation:


u=x^2
u^2=(x^2)^2\\u^2=x^4

Then,


u^2=64

Apply square root on both members


√(u^2)=√(64)\\u=8 , u=-8

Now substitute back
u=x^2

1.
x^2=8

2.
x^2=-8

Solving for x:

1.
x=+√(8)=√(2^3)=√(2^2).√(2)\\x=2√(2)\\or\\x=-√(8)\\x=-2√(2)

2.
x=+√(-8)=√((-1).8) =√(-1)√(8) \\x=i√(8)\\x=i.2√(2) \\or\\x=-√(-8)\\x=-i.2√(2)

Then the solutions for
x^4-64=0 are:


x_1=2√(2)\\x_2=-2√(2)\\x_3=i2√(2)\\x_4=-i2√(2)

To find the x intercepts of the graph
y=x^4-64 we have to replace with y=0.

This means:
x^4-64=0

We already found the solutions for the expression, but we have to consider only the real solutions.


x_1=2√(2)\\x_2=-2√(2)

Because in a graph we can't have imaginary solutions.

Then the x intercepts of the graph are:


A=(2√(2),0) and
B=(-2√(2),0)

The graph of the function is:

Find the solutions to x⁴-64=0 and the x-intercepts of the graph of y=x⁴-64.-example-1
User Mrsrinivas
by
8.5k points

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