In Exercises 91–100, find all values of x satisfying the given co...

Question

In Exercises 91–100, find all values of x satisfying the given conditions.

y = (x - 5)^(3/2) and y = 125

Accepted Answer

Hello. Today I'm going to be using these two statements to sulfur X. Now we're giving two quantities for why? Why is equal to the quantity X plus three? Race the five halves power and why is equal to Since Y is equal to both of these quantities. We can go ahead and set both of these quantities equal to each other. So doing so is going to give us X plus three raised to the five halves. Power is equal to 1024. Now in order to solve for X, we want to go ahead and rewrite this as a square root. So in order to do that we can rewrite this as the square root of X plus three raised to the fifth power. And that's going to be equal to 1024. Now what I want to go ahead and do is get this quantity outside of the square root. In order to do that. I can square both sides of this equation. Doing so is going to give me the quantity X plus three raised to the fifth power is equal to 1024 squared which gives me 1,048,576. And now I want to go ahead and get this quantity of X by itself in order to do that. I can go ahead and take the fifth root of both sides of this equation. Doing so is going to give me X plus three is equal to the fifth root of 1,048,576 and that's gonna be equal to 16. And finally I'm gonna go ahead and subtract three from both sides of this equation and X is equal to 13. Now, since X is equal to 13, I need to go ahead and verify that this works with our original equation. So I'm gonna go ahead and plug this in to the square root of X plus three to the fifth equal to 1024. And that's going to give me the quantity. 13 plus three rates to the fifth is equal to 1024. Well 13 plus three is going to give me 16. So I have the square root of 16 to the fifth, power is equal to 16 to the fifth is going to give me the square root of 1,048, is equal to 1024. And taking the square root of this number is going to give me 1, is equal to 1,024, which is a true statement and that means that X is equal to 13 is going to be our solution and the solution to this problem is going to be B So I hope this video helps you understanding how to solve this type of problem and I'll go ahead and see you all in the next video

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