Its impossilble to figure it out?

Question

Hi all

I want to know the cut point

y=√3x+1
y=3-x

I cant get near the answer if i draw it it shows me a real answer but it takes a lot of time to do that so i wanna calculate instead. Can someone explain this in a easy way please.

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2nd problem

2-x>√x


same prob cant get near the answer

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3rd and last problem

I want to know the comparison that gows to these points
(3,3) (10,6)

please explain it in a easy way



thank you very very very much!!!!

Answer 1

(3x)^1/2+1=3-x so (3x)^1/2= 2-x
1) x>=0( for the sqrt)
squaring both sides
3x= x^2-4x+4 so x^2-7x+4=0
x=((7+-sqrt(49-16))/2 = 7/2+-1/2sqrt(33)(both are positive)
If you meant
(3x+1)^1/2 =( 3-x)
3x+1>=0 s0 x>0-1/3
squaring 3x+1=x^2-6x+9
x^2-9x+8=0 and x=((9 +-sqrt(81-32))/2
2)As x^1/2>=0 2-x>=0 and x<=2 and also>=0
now you can square and
x^2-4x+2>x
x^2-5x+2>0 x= ((5+-sqrt(25-8))/2
With the limitations given above

0<=x < (5-sqrt(17))/2
3) I don´t understand what you are asking for