Find the value of x^0.5 + x^-0.5
unless you know what x is, it's kinda hard.
For example, if x = 9, then you have
√9 + 1/√9 = 3 + 1/3 = 10/3
x^0.5 + x^-0.5
is the same as √x + 1/√x
for which value of x are you evaluating it ?
To find the value of x^0.5 + x^-0.5, we need to understand the properties of exponents.
When dealing with exponents, x^a + x^b = x^(a+b) if the bases are the same.
In this case, we have x^0.5 + x^-0.5. Let's break it down:
x^0.5 represents the square root of x. Similarly, x^-0.5 represents the reciprocal of the square root of x.
So, x^0.5 + x^-0.5 can be rewritten as √x + 1/√x.
Now, we can simplify further. To do this, we need to rationalize the denominator by multiplying both the numerator and denominator of the second term by √x.
(√x + 1/√x) * (√x/√x) = (√x * √x + 1)/ √x
The numerator becomes x + 1 and the denominator stays as √x.
Therefore, x^0.5 + x^-0.5 simplifies to x + 1/√x, or x + 1/√x.