Thank you for your help.
11. 3/[SQRT(5) - 2]
14. SQRT(x + 4) = SQRT(x) - 2
14. square both sides to get
x+4 = x - 4√x + 4
√x = 0
x = 0
check:
LS = √4 = 2
RS = √0 - 2 = -2
LS is NOT equal to RS
so there is no solution.
Thank you.
How would i complete number 11, I have had alot of trouble with these types of equations. Please help.
the way you typed #11, it does not show an equation.
That is why I didn't touch it.
What do you want to do with it?
You're welcome! I would be happy to help you with your questions.
11. To simplify the expression 3/[SQRT(5) - 2], we need to rationalize the denominator. Rationalizing the denominator means getting rid of any square roots in the denominator. In this case, we have SQRT(5) - 2 in the denominator.
To rationalize the denominator, we can use the conjugate. The conjugate of SQRT(5) - 2 is SQRT(5) + 2.
To rationalize the denominator, we multiply both the numerator and the denominator by the conjugate:
3/[SQRT(5) - 2] * [SQRT(5) + 2]/[SQRT(5) + 2]
When we multiply the numerators and the denominators, we get:
3 * (SQRT(5) + 2) / [(SQRT(5))^2 - (2)^2]
Simplifying further:
3 * (SQRT(5) + 2) / (5 - 4)
Finally, this simplifies to:
3 * (SQRT(5) + 2) / 1
Which can be further simplified to:
3 * (SQRT(5) + 2)
So, the simplified expression is 3 * (SQRT(5) + 2).
14. To solve the equation SQRT(x + 4) = SQRT(x) - 2, we need to isolate the variable x.
First, square both sides of the equation to eliminate the square roots:
(SQRT(x + 4))^2 = (SQRT(x) - 2)^2
This simplifies to:
x + 4 = x - 4SQRT(x) + 4
Next, eliminate the x term on one side of the equation. In this case, we can subtract x from both sides:
x - x + 4 = x - x - 4SQRT(x) + 4
This simplifies to:
4 = -4SQRT(x)
Now, divide both sides by -4 to solve for SQRT(x):
4 / -4 = -4SQRT(x) / -4
This simplifies to:
-1 = SQRT(x)
Finally, square both sides again to solve for x:
(-1)^2 = (SQRT(x))^2
This simplifies to:
1 = x
Therefore, the solution to the equation SQRT(x + 4) = SQRT(x) - 2 is x = 1.