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.