In Exercises 115–122, find all values of x satisfying the given c...

Question

In Exercises 115–122, find all values of x satisfying the given conditions.y1 = x - 1, y2 = x + 4 and y1y2 = 14

Accepted Answer

Hello. Today we're going to sulfur X. Using the given conditions. So the first condition given to us is T. One is equal to the quantity X minus three. Our second condition is T two is equal to the quantity X minus one. And we are told that T one times T two plus one is equal to zero. So what we're going to go ahead and do is take our given T. One and T. Two and plug it in to this equation here. And we're gonna use this equation to sulfur X. Doing so is going to give us the quantity X minus three times the quantity X minus one plus one is equal to zero. And we're gonna go ahead and open up this pair of parentheses by foiling both of these quantities together. So doing so is going to give me X squared minus x minus three. X plus three plus one is equal to zero. And we need to go ahead and combine like terms while the combined herbal like terms here is going to be negative X and negative three X and positive three and positive one. And combining those terms together is going to give me X squared minus four. X plus four is equal to zero. Now this is a fact herbal trin Amiel as this is going to factor two, X minus two times X minus two is equal to zero. And we can go ahead and represent this as X - squared equal to zero because there are two instances of the quantity X -2. Now we're gonna go ahead and solve this for X. And in order to do that, we take the square root of both sides of the equation to cancel out the square and that's going to give me x minus two is equal to zero. And finally we're going to add two to both sides of the equation, and X is going to equal to two, which is going to be our solution for the given conditions. And that means that the solution to this problem is going to be be so. I hope this video helps you in 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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In Exercises 115–122, find all values of x satisfying the given conditions.y1 = x - 1, y2 = x + 4 and y1y2 = 14

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