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.f(x, y) = + − − , x, y ∈ R+ (y − 1x2 )2− −−−−−−−−−√ (x − 3 + (y − 4)2 )2

− −−−−−−−−−−−−−−√ +x2 y2− −−−−−√ (x − 1 +)2y2

− −−−−−−−−−−√Let

.

f(x, y) = + − − , x, y ∈ R+ (y − 1x2 )2− −−−−−−−−−−√ (x − 3 + (y − 4)2 )2

− −−−−−−−−−−−−−−√ +x2 y 2− −−−−−√ (x − 1 +)2

y 2− −−−−−−−−−−√

Then Max. of .f(x, y)

We can convert into Complex no. form ...::My Try− −−−−−−

Let , Then z = x + iy f(z) = |z − i| + |z − 3 − 4i| − |z| − |z − 1|

Now for Max., we use Inequality,△

But I did not understand in which pair i have used inequality.△

Help Required

Thanks

(algebra-precalculus)

asked Oct 18 '13 at 19:18

juantheron

5,991 2 9 24

– This just seems too py thagorean to me, but I dont know if that helps. chubakueno Oct 1 8 '1 3 at 22:36

1 Answer

let , we want have max ,but

, the "=" will hold when is on , ,the "=" will hold

when is , so MAX is ,when

A(0, 1), B(3, 4), C(0, 0), D(1, 0), P(x, y) PA + PB − PC − PD

PA − PC ≤ AC P AC PB − PD ≤ BD

P BD AC + BD = 1 + = 1 + 2(3 − 1 + (4 − 0)2 )2− −−−−−−−−−−−−−−√ 5√ P(0, −2)

answered Oct 20 '13 at 8:01

chenbai

3,970 4 16