HELP! i don't get this algebra 2 problem!?

Question

Solve.

a) x * x = 1

b) x * x = x
the answer is supposed to be {1, 0}??
can anyone tell me why it's {1, 0}?

c) x(x-1) = x(x+1)
the answer is {0}

Answer 1

Question a)
x ² = 1
x = ± 1

Question b)
x ² = x
x ² - x = 0
x (x - 1) = 0
x = 0 , x = 1

Question c)
x (x - 1) = x (x + 1)
x ² - x = x ² + x
- x = x
2x = 0
x = 0

Answer 2

B) Its because 1*1= 1....and 0 is the only answer other than 1 that with fit in. 0*0 = 0. It cant be 2 because 2*2 = 4. which isnt x*x=x

Answer 3

a) rewrite as x^2 - 1 = 0 which factors to (x-1)*(x+1) = 0 hence x = 1, -1
b) x*x = x can be rewritten as x*x - x = 0 which is also x*(x - 1) = 0. It is order 2 and so can have 2 solutions which are clearly 0 and 1.
c) x*(x-1) = x*(x+1) can be rewritten as
x*(x-1) - x*(x+1) = 0 which is x^2 - x - x^2 -x = 0 which is -2x = 0 and hence x = 0

Key insight is group all the terms onto one side of the = sign and then factor to get solutions.

Answer 4

A) X × X = 1 is the same as:

X² = 1

The only numbers that satisfy this condition are 1 and -1, as both squared are equal to 1.

B) X × X = X is the same as
X² = X
In this case, only the numbers 1 and 0 satisfy this condition, as they are the only numbers which, when multiplied by themselves, give the same result.

C) X(X-1) = X(X+1) is the same as
X² - X = X² + X
Zero (0) multiplied by itself is alwasy 0, adding or subtracting 0 will give the same result to both sides of this equation; only 0 satisfies this condition. Try using other numbers, positive or negative, to see why this is true.

Answer 5

a) x^2 = 1, then you take the square root of each side and get x = negative and positive 1.
b) divide each side by x. get x = 1
c) x^2 - x = x^2 + x
-2x = 0 divide by -2
x = 0

Answer 6

i'm not sure about it, but hope this helps.
a) x * x = 1
x² = 1
x =√ 1
x = 1

i dont know the rest....

Answer 7

A) x*1= 1

i think. what book is it in? cpm?