For what value of x is the equation 34+x4=1
true?
Responses
x=1
x is equal to 1
x=7
x is equal to 7
x=−7
x is equal to negative 7
x=−1
x is equal to negative 1
To find the value of x that makes the equation true, we need to solve the equation 34 + x^4 = 1.
Step 1: First, subtract 34 from both sides of the equation to isolate the x term:
x^4 = 1 - 34
x^4 = -33
Step 2: Since we are looking for real solutions, take the fourth root of both sides of the equation:
∛x^4 = (∛-33)
Step 3: Keep in mind that any real number raised to an even power will yield a positive result. Therefore, the equation has no real solutions because both sides of the equation will be positive.
Conclusion: The equation 34 + x^4 = 1 has no real solutions for x.
To find the value of x that makes the equation 34 + x^4 = 1 true, we need to solve the equation.
Step 1: Subtract 34 from both sides of the equation:
x^4 = 1 - 34 = -33
Step 2: Take the fourth root of both sides of the equation to isolate x:
∛(x^4) = ∛(-33)
Step 3: Since x can be a positive or negative value, we need to consider both possibilities.
For x = 1:
∛(1^4) = ∛(-33)
1 = -33, which is not true.
For x = 7:
∛(7^4) = ∛(-33)
7 = -33, which is not true.
For x = -7:
∛((-7)^4) = ∛(-33)
-7 = -33, which is not true.
For x = -1:
∛((-1)^4) = ∛(-33)
1 = -33, which is not true.
Therefore, there is no value of x that makes the equation true.