Find the coordinates of the points of intersection of the two curves. (y=x^2-1 & y=6/x^2)?

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Answer 1 · 2018-04-17T10:11:56

$(-sqrt3,2) " , "(sqrt3,2)$

$y=x^2-1$

$y=6/x^2$

by solving the two equations simultaneously

$x^2-1=6/x^2$

$x^4-x^2-6=0$

Factorize

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

$x^2=3$ $" , "$ $color(red)(x^2=-2 " refused as it's solution is not real"$

$x=+-sqrt3$

Substitute in any of the equations to find the $y$ coordinates of the points of intersection

$f(-sqrt3)=2$ $" , "$ $f(sqrt3)=2$

so the two points of intersection will be:

$(-sqrt3,2) " , "(sqrt3,2)$

I hope this was helpful.