1/(X^-2Y)-1(XY^-2)=____
XY
(square root of 84 - square root of 5.25)
I don't understand the first equation.
sqrt(84)=sqrt(4*21)=sqrt(16*5.25)=4sqrt(5.25)
so
sqrt(84)-sqrt(5.25)=
4sqrt(5.25)-sqrt(5.25)=3sqrt(5.25)
To solve the first equation 1/(X^-2Y)-1(XY^-2), we need to simplify it.
First, let's simplify the expression by applying the negative exponents:
1/(X^-2Y) - 1(XY^-2) is equal to X^2Y - XY^2.
Now, we can combine like terms by factoring out XY:
XY(X - Y).
Therefore, the solution for the first equation is XY(X - Y).
Moving on to the second question about finding the value of sqrt(84) - sqrt(5.25):
To simplify sqrt(84), we look for perfect square factors of 84. Since 4 is a perfect square factor of 84, we can rewrite sqrt(84) as sqrt(4 * 21).
Using the property sqrt(a * b) = sqrt(a) * sqrt(b), we can simplify:
sqrt(4) * sqrt(21) = 2 * sqrt(21).
Now, let's simplify sqrt(5.25). Since 5.25 is not a perfect square, we can express it as sqrt(5.25) directly.
Now, we can substitute the simplified values back into the original equation:
sqrt(84) - sqrt(5.25) = 2 * sqrt(21) - sqrt(5.25).
We can now simplify the expression further by recognizing that both terms have sqrt(5.25). We can combine these terms:
2 * sqrt(21) - sqrt(5.25) = sqrt(5.25) * (2 - 1).
Simplifying 2 - 1, we have:
sqrt(5.25) * 1 = sqrt(5.25).
Therefore, the value of sqrt(84) - sqrt(5.25) is equal to sqrt(5.25) or 3 * sqrt(5.25).