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anonymous
 5 years ago
solve this quadratic system:
4x^2 + 9y^2 = 72
x  y^2 = 1
explain please?
anonymous
 5 years ago
solve this quadratic system: 4x^2 + 9y^2 = 72 x  y^2 = 1 explain please?

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amistre64
 5 years ago
Best ResponseYou've already chosen the best response.1they want to know what points they have in common

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.172 from each side of the top one and +1 to both sides of the bottom one and you will have 2 equations equal to 0

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.1since both equation = 0; they equal each other; so make them equal and subtract one equation from the other

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.14x^2 + 9y^2 72 = x  y^2 +1 4x^2 + 9y^2 72 x + y^2 1  4x^2 x +10y^2 73 = 0 but i might be trying to do this the ahard way

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.1try this: 4x^2 + 9y^2 = 72 x  y^2 = 1 (*9) 4x^2 + 9y^2 = 72 9x  9y^2 = 9  4x^2 +9x = 63 4x^2 =9x 63 = 0 ; solve the quadratic now

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.14x^2 +9x 63 = 0 x = 9/8 + sqrt(81 4(4)(63))/8 x = 9/8  sqrt(81 4(4)(63))/8

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.1x = 9/8 + sqrt(1089)/8

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.1x = 9 + 33  8

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.1x = 24/8 = 3 x = 42/8 = 21/4 = 5.25

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.1plug these into one of the equations to solve for y

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0For what it's worth, you were (in my opinion) doing it the hard way (not that it makes much difference): \[x  y^2 = 1 \implies y^2 = x+1\] Which we can then use in the first equation: \[4x^2+9(x+1)=72 \implies ... \]

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.172+9 = 63 .... yay!! .. validation ;)

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Note when finding all solutions \[y^2 = x+1 \implies y=\pm \sqrt{x+1}\] so it will lead to 4 (x,y) pairs.

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.1yeah, that first bit was definetly going down the wrong path... lol

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.1a parabola joined to an ellipse i think would produce at most 2 real points. right?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0(Maybe they aren't all real, hehe!)

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.1i saw it wrong there for a moment :)
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