SOLUTION: Please help me!!!I have this problem and I do not have any idea how to go about solving. If x= radical 6/7, then evaluate (x + 1/x)exponient 2.....I hope this makes sense..I didn't

Algebra ->  Radicals -> SOLUTION: Please help me!!!I have this problem and I do not have any idea how to go about solving. If x= radical 6/7, then evaluate (x + 1/x)exponient 2.....I hope this makes sense..I didn't      Log On


   

Question 132974: Please help me!!!I have this problem and I do not have any idea how to go about solving. If x= radical 6/7, then evaluate (x + 1/x)exponient 2.....I hope this makes sense..I didn't know how to type it in exactly..Any help would be greatly appreciated.. Thankyou Angie
Found 2 solutions by solver91311, josmiceli:
Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!
All you need to do is substitute the given value for x into the expression and then do the arithmetic.

If you meant x=sqrt%286%2F7%29, then evaluate %28x%2B1%2Fx%29%5E2, that means you need to evaluate:

%28sqrt%286%2F7%29%2B1%2Fsqrt%286%2F7%29%29%5E2

Apply FOIL:


6%2F7%2B1%2B1%2B%281%2F%286%2F7%29%29=6%2F7%2B2%2B7%2F6

LCD is 42, so:
36%2F42%2B84%2F42%2B49%2F42=169%2F42

Since 169 (13 * 13) and 42 (2 * 3 * 7) have no common factors, this is reduced to lowest terms.

On the other hand, if you meant: x=sqrt%286%29%2F7, then evaluate %28x%2B1%2Fx%29%5E2, that means you need to evaluate:

%28sqrt%286%29%2F7%2B1%2F%28sqrt%286%29%2F7%29%29%5E2

Apply FOIL:


6%2F49%2B1%2B1%2B%281%2F%286%2F49%29%29=6%2F49%2B2%2B49%2F6

LCD is 294, so:
36%2F294%2B588%2F294%2B2401%2F294=3025%2F294

Since 3025 (5 * 5 * 11 * 11) and 294 (2 * 3 * 7 * 7) have no common factors, this is reduced to lowest terms.

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
x+=+sqrt%286%2F7%29
%28x+%2B+1%2Fx%29%5E2+=+x%5E2+%2B+2+%2B+%281%2Fx%29%5E2


6%2F7+%2B+2+%2B+7%2F6+=+%2836+%2B+84+%2B+49%29%2F42
169%2F42 answer
check:
x+=+sqrt%286%29%2Fsqrt%287%29
x+=+.9258
%28x+%2B+1%2Fx%29%5E2+=+%28.9258+%2B+1.080%29%5E2
%28.9258+%2B+1.080%29%5E2+=+4.0237
169%2F42+=+4.0238
close enough