SOLUTION: Q. If x-1/x=3 find the value of 1. x^4+1/x^4 2. X^2+1/x^2 3. (X+1/x)^2 Q. if a+1/a=7 find the value of 1.a^2+1/a^2 2.(a-1/a)^2 3. a^4+1/a^4 Q. If x+1/x=4, show that

Algebra ->  Average -> SOLUTION: Q. If x-1/x=3 find the value of 1. x^4+1/x^4 2. X^2+1/x^2 3. (X+1/x)^2 Q. if a+1/a=7 find the value of 1.a^2+1/a^2 2.(a-1/a)^2 3. a^4+1/a^4 Q. If x+1/x=4, show that       Log On


   

Question 1092206: Q. If x-1/x=3 find the value of
1. x^4+1/x^4 2. X^2+1/x^2 3. (X+1/x)^2
Q. if a+1/a=7 find the value of
1.a^2+1/a^2 2.(a-1/a)^2 3. a^4+1/a^4
Q. If x+1/x=4, show that x^2+1/x^2=14
Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!

I'll show you a couple of these so you can get the idea of how to work them. Then you can try the others yourself.

The last question is the easiest one to use to show you the general concept for working this kind of problem. In that problem we are given

x+%2B+1%2Fx+=+4

and we are to show that

x%5E2+%2B+1%2Fx%5E2+=+14

Observe what happens when you square both sides of the given equation. When you square the binomial on the left, the middle term is a constant. That is the general principle that lets you solve problems like this.

%28x+%2B+1%2Fx%29%5E2+=+4%5E2
x%5E2+%2B+2+%2B+1%2Fx%5E2+=+16
x%5E2+%2B+1%2Fx%5E2+=+14

Now let's look a bit at your second problem. There you are given

a%2B1%2Fa+=+7

and you are asked to find the values of

1. a^2+1/a^2
2.(a-1/a)^2
3. a^4+1/a^4

Finding the first of these will be exactly like the example worked above. For the second one, note that

%28a-1%2Fa%29%5E2+=+a%5E2-2%2B1%2Fa%5E2

so that one will be easy after you have solved the first one. And for the third of these, you can get the answer in a similar fashion by squaring your answer for the first one.