# Abstract Inequalities

• October 26th 2012, 10:17 AM
GrigOrig99
Abstract Inequalities
Can anyone help me confirm if I've solved this correctly?

Many thanks.

Q.
If $a^2+b^2=1$ & $c^2+d^2=1$, show that ac + bd < 1.

Attempt: $a^2+b^2+c^2+d^2=2$
if $a^2+c^2\geq2ac$ & $b^2+d^2\geq2bd$
if $2ac+2bd\leq2$
if $ac+bd\leq1$...true
• October 26th 2012, 10:22 AM
HallsofIvy
Re: Abstract Inequalities
Yes, that is a perfectly good proof.

(Of course, $a^2+ c^2\ge 2ac$ because $(a- c)^2= a^2- 2ac+ c^2\ge 0$.)
• October 26th 2012, 11:35 AM
GrigOrig99
Re: Abstract Inequalities
Great. Thank you.