SOLUTION: a. Find all (real) solutions for x: x − √(6 − x) = 4. If you eliminate a solution, show or explain why. b. Jill wants to make a substitution in the equation x^

Algebra ->  Equations -> SOLUTION: a. Find all (real) solutions for x: x − √(6 − x) = 4. If you eliminate a solution, show or explain why. b. Jill wants to make a substitution in the equation x^      Log On


   

Question 907343: a. Find all (real) solutions for x: x − √(6 − x) = 4. If you eliminate a solution, show or explain why.
b. Jill wants to make a substitution in the equation x^(1/3) – 36 = 9x^(1/6)
in order to convert it to a quadratic
equation. Give the substitution (in the form t = …) and the resulting quadratic equation. Do not
solve.
c. After making the substitution u = x^4 in an equation, Jaime found the solutions u = 16 and
u = -4. Find the solution(s) for x.
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
x-sqrt%286-x%29=4
x-4=sqrt%286-x%29
%28x-4%29%5E2=6-x
x%5E2-8x%2B16=6-x
x%5E2-7x%2B10=0
%28x-2%29%28x-5%29=0
Two solutions:
x-2=0
x=2
and
x-5=0
x=5
Verify the solutions.
2-sqrt%286-2%29=4
2-sqrt%284%29=4
2-2=4
0=4
Not a solution.
5-sqrt%286-5%29=4%7D%7D%0D%0A%7B%7B%7B5-sqrt%281%29=4
5-1=4
4=4
Good solution.
highlight%28x=5%29
.
.
.
x%5E%281%2F3%29+%96+36+=+9x%5E%281%2F6%29
x%5E%281%2F3%29-+9x%5E%281%2F6%29-36=0
Substitute,
t=x%5E%281%2F6%29
t%5E2=x%5E%281%2F3%29
highlight%28t%5E2-9t-36=0%29
.
.
.
u=x%5E4
16=x%5E4
highlight%28x=2%29 and highlight%28x=-2%29
and
x%5E4=-4
I'm assuming you aren't looking for complex solutions but only real solutions.
There are no real solutions.