How to find second intersection point?

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Amanda
Amanda 2022-9-17
评论： Star Strider 2022-9-17
Okay, so
My task is to find the intersections points of functions f1 = 1/x and f2 = sqrt(5./2 - (x^2))
I've found one of the intersections points using:
Intersections=find(abs(f1-f2)<=(0.05));
xvalues=x1(Intersections);
But looking at the graphs I see there are two intersections points, so how do I find the other?

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回答（2 个）

Star Strider
Star Strider 2022-9-17
Ran in:
It is easiest to do this symbolically —
syms x
f1 = 1/x;
f2 = sqrt(5./2 - (x^2));
Intx = solve(f1 == f2)
Intx = 
Intxd = double(Intx)
Intxd = 2×1
1.4142 0.7071
.
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Amanda
Amanda 2022-9-17
I tried using your code, and got the same values of x. However, looking at the graph, the second x-value is incorrect. We get x = 1.4142, while it seems to be more 1.387
Star Strider
Star Strider 2022-9-17
The symbolic approach solves for and , agreeing with the numeric approach, so I do not see how any other values could be correct.

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Torsten
Torsten 2022-9-17
Ran in:
x1 = 0:0.0001:1.5;
f1 = 1./x1;
f2 = sqrt(5./2 - (x1.^2));
Intersections = find(abs(f1-f2)<0.00005);
xvalues=x1(Intersections)
xvalues = 1×2
0.7071 1.4142

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