Mathematics
OpenStudy (anonymous):

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 ___________.

OpenStudy (anonymous):

is that A square or a square

OpenStudy (anonymous):

Sorry, refer A=a

OpenStudy (anonymous):

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 $$2\sqrt2$$

OpenStudy (anonymous):

I am with $$2\sqrt2$$.

OpenStudy (anonymous):

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

OpenStudy (anonymous):

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

OpenStudy (anonymous):

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