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# i just need help with this last one

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1 i just need help with this last one

Nov 6, 2019

#1
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3x^2 - 4y^2 + 4x -8y + 4  =  0

3x^2  +y^2  + 4x -3y + 4  = 0

Subtract the first equation from the second and we get that

5y^2  + 5 y   =   0   divide through by  5

y^2 + y  = 0       factor

y ( y + 1)   =   0

Setting   each  factor  to 0   and solving for  y  produces  :

y  =  0      and  y   =  -1

When y  =  0

We have that both equations evaluate to

3x^2 + 4x + 4  = 0    (1)

This has no real solutions for  x   when y  = 0 because the discriminant for (1)  is less than  0

So....there  are no real intersection points  when  y  = 0

When  y  =  -1

The first equation evaluates to

3x^2 - 4 + 4x + 8 + 4  =  0

3x^2 + 4x + 8  = 0       (2)

And the second equation evaluates to

3x^2 + 1 + 4x + 3 + 4  = 0

3x^2 + 4x +  8  =  0    (3)

(2)  and (3)  are the same

Again  when y  =  -1  there are no real solutions for x because  the discriminant is less than 0

So....we  have no  real  solutions   in x  for either y value....

WolframAlpha confirms this   :  https://www.wolframalpha.com/input/?i=3x%5E2+-+4y%5E2+%2B+4x+-8y+%2B+4++%3D+0%2C+++3x%5E2++%2By%5E2++%2B+4x+-3y+%2B+4+%3D+0++   Nov 6, 2019
edited by CPhill  Nov 6, 2019
edited by CPhill  Nov 6, 2019