00:01
For this question, they're asking us to find the exact solution for each equation, find the approximate solution to the nearest tenth.
00:10
And the equation they give us is square root 2 minus 1 over square root 2 plus 1 is equal to x over 2.
00:22
In this situation here, i want to isolate my variable as quickly as possible, so i'm going to multiply both sides by 2.
00:30
Okay um and then i have to distribute that two on the top here inside of my numerator so uh two square root two minus two over square root two plus one is equal to x i've isolated my variable i do need to now make sure that my answer uh is in proper simplified form just because i don't want any radicals in the basement.
01:05
So in order to get rid of the radical in the basement, i need to multiply both the top and the bottom of my fraction by the conjugate of my denominator.
01:13
So if it's square root 2 plus 1, the conjugate would be square root 2 minus 1.
01:19
On the top and the bottom here, i just want to make sure the square root is only on the 2, not on the negative 1.
01:27
All right.
01:29
And then i just, there's lots of foiling going to happen.
01:32
Here.
01:36
So here i do square root two times two square root two gives me two times two.
01:42
Square two times negative two is negative two square root two.
01:47
Negative one times two square root two is negative two square root two.
01:53
And negative one times negative two is positive two.
01:58
Okay, and we'll simplify that in a second here...