+25 Solve the following equation
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sqrt of x-4 - sqrt of x-4 to the 4th power=12
The solution(s) of the given equation is/are x=??
If you want an equation version then :\( \sqrt {x-4}- \sqrt[4]{x-4}=12\)
x=260
Solve for x:
sqrt(x-4)-(x-4)^(1/4) = 12
Subtract 12 from both sides:
-12-(x-4)^(1/4)+sqrt(x-4) = 0
Simplify and substitute y = -(x-4)^(1/4):
-12-(x-4)^(1/4)+sqrt(x-4) = -12-(-(x-4)^(1/4))+(-(x-4)^(1/4))^2 = y^2-y-12 = 0:
y^2-y-12 = 0
The left hand side factors into a product with two terms:
(y-4) (y+3) = 0
Split into two equations:
y-4 = 0 or y+3 = 0
Add 4 to both sides:
y = 4 or y+3 = 0
Substitute back for y = -(x-4)^(1/4):
-(x-4)^(1/4) = 4 or y+3 = 0
Multiply both sides by -1:
(x-4)^(1/4) = -4 or y+3 = 0
Raise both sides to the power of four:
x-4 = 256 or y+3 = 0
Add 4 to both sides:
x = 260 or y+3 = 0
Subtract 3 from both sides:
x = 260 or y = -3
Substitute back for y = -(x-4)^(1/4):
x = 260 or -(x-4)^(1/4) = -3
Multiply both sides by -1:
x = 260 or (x-4)^(1/4) = 3
Raise both sides to the power of four:
x = 260 or x-4 = 81
Add 4 to both sides:
x = 260 or x = 85
sqrt(x-4)-(x-4)^(1/4) => sqrt(85-4)-(85-4)^(1/4) = 6:
So this solution is incorrect
sqrt(x-4)-(x-4)^(1/4) => sqrt(260-4)-(260-4)^(1/4) = 12:
So this solution is correct
The solution is:
Answer: |
| x = 260
