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## Homework Statement

Prove that [tex]\left(ab+cd\right)^{2} \leq \left(a^{2}+c^{2}\right)\left(b^{2}+d^{2}\right)[/tex]

## Homework Equations

None

## The Attempt at a Solution

I've broken the LHS down to the following:

[tex]\left(ab\right)^{2}+2abcd+\left(cd\right)^{2} [/tex]

The RHS:

[tex]\left(ab\right)^{2} + \left(ad\right)^{2} + \left(bc\right)^{2} + \left(cd\right)^{2}[/tex]

So, ultimately... it works out that I need to show [tex]2abcd \leq \left(ad\right)^{2} + \left(bc\right)^{2}[/tex]

This is where I'm getting stuck... Any suggestions...