Some questions, Doing via corresponence so need help! (1 Viewer)

[KimmorleyKiller]

Im doing ext1 via correspondence, but apparently this is 2u stuff anyway I need help with it, so working out would be a great help

Express with rational denominator: 1+ Root 8 / 1+3 root 2
 
express 4/25 + 213/7000
 
solve for x(2-x) > -3
 
solve |2x+1|<|2x-1|
 
Factorise 250-2x^3
 
|2x+1|>x

Lol i got infinite for the above one

Cheers for your help guys, KK

 

[yinyin]

hm... the last one:
x=-1 , x= -1/3
|2x+1| same as 2x + 1 just 2x-1=x therefore x=1
-|2x+1|= -2x-1=x
-1=3x
x=-1/3
i not sure...

 

[pLuvia]

Express with rational denominator: 1+ Root 8 / 1+3 root 2
Just multiply both numerator and denominator by 1-3root2 and you should end up with a rationalised fraction

express 4/25 + 213/7000

simple fraction addition?

solve for x(2-x) > -3

Expand out the brackets and factorise and you should end up with 2 answers. Can use a test point to make sure which way the sign goes

solve |2x+1|<|2x-1|

Graphing this out would be easier to find the solutions

Factorise 250-2x^3

Divide by 2 end up with 125-x³ then using this rule (x³-a³) = (x²+ax+a²) you can factorise it

|2x+1|>x

2x+1 > x
2x+1 < -x

Then solve

 

[yinyin]

haha learn sumthing new...
thanks

 

[SoulSearcher]

solve |2x+1|<|2x-1|

you can either graph this one, or square both sides to solve this

i.e
(2x+1)² < (2x-1)²
4x² + 4x + 1 < 4x² - 4x + 1
4x < -4x
8x < 0
x < 0
test x = -1 to see if this is true
| -2 + 1 | < | -2 - 1 |
1 < 3
therefore x < 0

 

[Elke]

Hey I'm doing 3 unit too, but am having difficulty with the basic 2 unit bit and am thinking of dropping back to 2 unit.

I'm having trouble with xy = 4 , 2x-y-7= 0 simultaneously and

factorising 2x^2 -3x + 1= 0

I'm begging my parents for a tutor but they wont budge, so I'm on my lonesome doing textbook exercises!


any simple working or words of advice would be greatly appreciated.

 

[webby234]

xy = 4
y = x/4

Substitute into second equn
2x - x/4 - 7 = 0
8x - x = 28
x = 4
y = 1

2x^2 -3x + 1= 0
(2x - 1) (x - 1) = 0

 

[Mountain.Dew]

damn...beat me to it

xy = 4...(1)
2x-y-7= 0...(2)

now y = 4/x (1) ==> sub into (2)

2x - [4/x] - 7 = 0

so 2x^2 - 4 - 7x = 0

2x^2 - 7x - 4 = 0

(x-4)(2x+1) = 0

so, x = 4, -1/2 <== sub those values back into (1) ==> y = 1, -8 respectively.

factorising 2x^2 -3x + 1= 0...

think about the 'cross' method:

2 -1 --> -2
\ /
X
/ \
1 -1 --> -1

seems to work ==> therefore 2x^2 -3x + 1 = (2x-1)(x-1)

 

[Mountain.Dew]

xy = 4
y = x/4

small problem there...dunno how u got the right answer though...lol

 

[SoulSearcher]

Each person to thier own method. If it works, its good enough, although I don't know how webby234 got the right answer.

Hehe, unless you don't know that BOS exists.

 

[webby234]

Oops - I solved it by looking at it then thought i had better do some working. And then when I checked it by substituting the values into the original equation it was right.
I think the reason I still got the right answer is that y = 1
and 1/y should = x/4 not y = x/4 but this doesnt matter in this case as 1/y = y.

 

[Elke]

Thanks SO much webby234, Mountain.Dew, Iruka, it was a big help!