SOLUTION: Hi,
Please help me solve this equation involving negative rational exponents: {{{ 3z^-1-3z^(-1/2)+1= 0 }}}.
Here are the steps I took to try to solve the problem:
First,
Algebra ->
Equations
-> SOLUTION: Hi,
Please help me solve this equation involving negative rational exponents: {{{ 3z^-1-3z^(-1/2)+1= 0 }}}.
Here are the steps I took to try to solve the problem:
First,
Log On
Question 1127154: Hi,
Please help me solve this equation involving negative rational exponents: .
Here are the steps I took to try to solve the problem:
First, I used the substitution method using "u" and tried completing the square and got .
Then, I used the quadratic equation and got 1/ 2 plus or minus 3i sqrt( 3 ) / 2.
Last I tried solving for x^-1/2 to get the final answer, but I cannot yield the books' answer: 3 / 2 plus or minus 3i sqrt( 3 ) / 2.
Can you please help me know where I am going wrong? Thank you. Answer by ikleyn(52776) (Show Source):
The equation is
- + 1 = 0.
Multiply by z both sides. You will get
= 0, or, equivalently,
= 0.
Now introduce new variable u = . The last equation will take the form
= 0.
Apply the quadratic formula
= = = .
Now consider separately both cases
a) u = = . Hence, squaring, you get
z = = = = ,
and
b) u = = . Hence, squaring, you get
z = = = = .
Answer. There are two solutions. They are complex numbers
and .
Solved.
----------------
Surely, it can be done in many ways and on different paths.
