(x,y,z) belongs to R^3 are points that lie on the plane x+2y+3z=78, and lie on the sphere x^2+y^2+z^2=468. The maximum value of x has the form a/b, where a and b are coprime positive integers. What is the value of a+b?
(x,y,z) belongs to R^3 are points that lie on the plane x+2y+3z=78, and lie on the sphere x^2+y^2+z^2=468. The maximum value of x has the form a/b, where a and b are coprime positive integers. What is the value of a+b?
What thoughts have you had about this? We need to see what YOU have done!
Just some thoughts to get you started.
The sphere is about the origin.
The intersection of the plane with the sphere (if any) is a circle.
Consider the point on the plane that is nearest the origin.
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