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 ___________.

Question

anonymous · Answer

is that  A square or a square

anonymous · Answer

Sorry, refer A=a

anonymous · Answer

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 $2\sqrt2$

anonymous · Answer

I am with $2\sqrt2$.

anonymous · Answer

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

anonymous · Answer

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

anonymous · Answer

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