SOLUTION: Solve for the following pronumerals: a) 9^1/x = 3sqrt(3) b) 2sqrt(6) - sqrt(2) = sqrt(a-b sqrt(3)) c) 1/ 3-sqrt(8) = a + b sqrt(2)

Algebra ->  Equations -> SOLUTION: Solve for the following pronumerals: a) 9^1/x = 3sqrt(3) b) 2sqrt(6) - sqrt(2) = sqrt(a-b sqrt(3)) c) 1/ 3-sqrt(8) = a + b sqrt(2)      Log On


   

Question 1117329: Solve for the following pronumerals:
a) 9^1/x = 3sqrt(3)
b) 2sqrt(6) - sqrt(2) = sqrt(a-b sqrt(3))
c) 1/ 3-sqrt(8) = a + b sqrt(2)
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
a) 9%5E%221+%2F+x%22%22=%223sqrt%283%29
%283%5E2%29%5E%221+%2F+x%22%22=%223%2A3%5E%221+%2F+2%22
3%5E%222+%2F+x%22%22=%223%5E%221+%2B+1+%2F+2%22
3%5E%222+%2F+x%22%22=%223%5E%223+%2F+2%22
2%2Fx=3%2F2
2%2A2%2F3=x
highlight%28x=4%2F3=1%261%2F3%29

b) 2sqrt%286%29+-+sqrt%282%29+=+sqrt%28a-b%2Asqrt%283%29%29
When solving, we can square both sides,
as long as we check for possible extraneous solutions later.
%282sqrt%286%29+-+sqrt%282%29%29%5E2+=+a-b%2Asqrt%283%29%29

2%5E2%2A6-+4sqrt%2812%29%2B2+=+a-b%2Asqrt%283%29
4%2A6-+4sqrt%284%2A3%29%2B2+=+a-b%2Asqrt%283%29
24-+4sqrt%284%29sqrt%283%29%2B2+=+a-b%2Asqrt%283%29
26-+4%2A2sqrt%283%29+=+a-b%2Asqrt%283%29
26-+8sqrt%283%29+=+a-b%2Asqrt%283%29 ---> highlight%28system%28a=26%2Cb=8%29%29

c) If it is 1/ 3-sqrt(8) = a + b*sqrt(2)
1%2F+3-sqrt%288%29+=+a+%2B+b%2Asqrt%282%29
1%2F+3-sqrt%284%2A2%29+=+a+%2B+b%2Asqrt%282%29
1%2F+3-sqrt%284%29%2Asqrt%282%29+=+a+%2B+b%2Asqrt%282%29
1%2F+3-2sqrt%282%29+=+a+%2B+b%2Asqrt%282%29 ---> highlight%28system%28a=1%2F3%2Cb=2%29%29

If it is 1/(3-sqrt(8)) = a + b*sqrt(2)
1%2F%283-sqrt%288%29%29+=+a+%2B+b%2Asqrt%282%29
%281%2F%283-sqrt%288%29%29%29%28%283%2Bsqrt%288%29%29%2F%283%2Bsqrt%288%29%29%29%22=%22a+%2B+b%2Asqrt%282%29
%283%2Bsqrt%288%29%29%2F%28%283-sqrt%288%29%29%283%2Bsqrt%288%29%29%29%22=%22a+%2B+b%2Asqrt%282%29
%283%2Bsqrt%288%29%29%2F%283%5E2-%28sqrt%288%29%29%5E2%29%22=%22a+%2B+b%2Asqrt%282%29
%283%2Bsqrt%288%29%29%2F%289-8%29%22=%22a+%2B+b%2Asqrt%282%29
%283%2Bsqrt%288%29%29%2F1%22=%22a+%2B+b%2Asqrt%282%29
%283%2Bsqrt%288%29%29%22=%22a+%2B+b%2Asqrt%282%29
%283%2Bsqrt%284%2A2%29%29%22=%22a+%2B+b%2Asqrt%282%29
%283%2Bsqrt%284%29%2Asqrt%282%29%29%22=%22a+%2B+b%2Asqrt%282%29
%283%2B2%2Asqrt%282%29%29%22=%22a+%2B+b%2Asqrt%282%29 ---> highlight%28system%28a=3%2Cb=2%29%29