Equating like entries: xy^2 z^2 = λx x^2 yz^2 = λy x^2 y^2 z = λz.
Hence, x^2 y^2 z^2 = λx^2 = λy^2 = λz^2.
(i) If λ = 0, then at least one of x, y, z is 0, and thus f(x,y,z) = 0 <---Minimum (Note that there are infinitely many such points.) (f being a perfect square implies that this has to be the minimum.)
(ii) Otherwise, we have x^2 = y^2 = z^2. Substituting this into g yields 3x^2 = 289 ==> x = ±17/√3.
This yields eight critical points (all signage possibilities) (x, y, z) = (±17/√3, ±17/√3, ±17/√3), and f(±17/√3, ±17/√3, ±17/√3) = (289/3)^3 <----Maximum
Stare at the numbers. Especially the first two. First one is -11. Second is . Let's guess you keep multiplying. . Smells correct, let's confirm with the last one: . I think we found a pattern. Each element is 7 times the previous one. With some practice you can just write the function, else let's divide by -11 away and let's see what we get:
. Basically, the exponent is 1 less than the value we're evaluating the function. That leads tho the following
A trapezoid is a quadrilateral with only one pair of opposite sides parallel. The parallel sides are called bases, and the nonparallel sides are called legs. A segment that joins the midpoints of the legs is called the median of the trapezoid
