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19 Jul 2008, 13:16
Kudos
Bookmarks
Hii all,
a quick question - when u are substituting numbers in a question when do you use the same number and different numbers for x and y.
for ex... they ask what is the value of x^ 3- y ^ 3 when x^2 + y^2 is at a minimum? in the explanations they used same value for x and y and said the answer should be 0.
please explain....
a quick question - when u are substituting numbers in a question when do you use the same number and different numbers for x and y.
for ex... they ask what is the value of x^ 3- y ^ 3 when x^2 + y^2 is at a minimum? in the explanations they used same value for x and y and said the answer should be 0.
please explain....
22 Jul 2008, 09:11
Kudos
Bookmarks
the trick to this question is to look at the restriction they place on x and y
in the example, you are to examine "when x^2 + y^2 is at a minimum"
since all (real) numbers are positive when squared, the way to minimize this expression is to look at where x^2 and y^2 are the least, which will always be at zero (0).
thus, the answer to x^3-y^3 will be 0-0 or 0.
in general, you can use the same values for x and y when there is no substantive difference between them in the formula. for example, in the formula (x+y) / xy , x and y can be switched without effect. whereas in (x-y) / xy , they cannot be interchanged.
in the example, you are to examine "when x^2 + y^2 is at a minimum"
since all (real) numbers are positive when squared, the way to minimize this expression is to look at where x^2 and y^2 are the least, which will always be at zero (0).
thus, the answer to x^3-y^3 will be 0-0 or 0.
in general, you can use the same values for x and y when there is no substantive difference between them in the formula. for example, in the formula (x+y) / xy , x and y can be switched without effect. whereas in (x-y) / xy , they cannot be interchanged.
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