can you help me with my algebra issues?

Question

Will someone show me how to arrive at the solutions to these problems please? We have to use the quadratic formula to solve i believe.

(x-1)^2 = 8


x / x - 1 + 1/x = 2

Thanks in advance, im hoplessly lost currently

Answer 1

(x - 1)² = 8

(x - 1)² = √8

(x - 1)² = √4 √2

(x - 1)² = 2√2

x - 1 = 2√2

x = 1 ± 2√2

Answer 2

OR, if you really want to use the quadratic formula,

1) (x-1)^2 = x^2 - 2x +1 = 8 or x^2 - 2x -7 = 0 --(solve with quadratic formula)

2) Too simple to use the q/f

Answer 3

the easiest way to do the first problem is take the square root of both sides and subtract 1 on both sides *but* remember that when you take the square root of a number you get + or - the square root of that number so it would be....

x=(+ or -)sqrt(8) - 1

then do this for the second...
create a least common denominator
(x/x)*x /( x - 1) + [(x-1)/(x-1)]*1/x = 2
x^2/[x^2-x)] + (x-1)/[x^2-x)] = 2
then multiply the least common denominator on both sides
x^2 + x - 1 = 2x^2 - 2x
set equal to zero
x^2 - 3x + 1 = 0
use quadratic formula
x=[3(+ or -)sqrt(3^2 - 4(1)(1))]/2(1)
then solve

sorry this looks really confusing because its on the computer try to write it out on a piece of paper

Answer 4

One at a time... (x-1)^2 = 8 taking the sq root of both sides gives us x-1 = 8^(1/2).. now add 1 to both sides to get...
x=8^(1/2)+1 therefore x=3.828 no quad eq. req'd

x/x-1 +1/x =2 well x/x is 1 right and 1-1 is zero therefore...
1-1+1/x=2
1/x=2
Multiply by x (both sides) to get 2x=1 so x=1/2

Answer 5

step by step for #1

(x-1)=Sqrt(8)

x=Sqrt(8)-1


#2

(x/(x-1))(x/x)+(1/x)((x-1)/(x-1))=2

(x^2+x+1)/(x^2+x)=2

at this point, i'd drop it into mathimatica or a similar program i don't have on my computer

Answer 6

I wish I could but I loaned out the numbers on my keyboard.