Question

A, b, c ,d are real numbers. If a square + b square is less than or equal to 2, and c square + d square is less than or equal to 4, the maximum value of the expression ac+bd is ___________.

Answer 1

is that A square or a square

Answer 2

Sorry, refer A=a

Answer 3

Okay I think \(2\sqrt2\) must be the answer \(a^2 + b^2 \le 2\) so I take b=0 for a to be max. and similarly in \(c^2 + d^2 \le 4\) I take d=0 and I get \(2sqrt2\).
Even if I split in equal halves I am still getting \(2\sqrt2\)

Answer 4

I am with \(2\sqrt2\).

Answer 5

I did like this. I took a=b=1, c=d=2, so that overall, we may the product maximum, i.e. 4

Answer 6

Not possible If \(c=d=2\). Then, \(c^2 +d^2 = 4 +4 = 8 \) which does not satisfy \(c^2 + d^2 \le 4\).

Answer 7

Oh my God, I wrote this answer itself.. Anyways, thanks for ur reply