# [SOLVED]Inequality involving a, b, c and d

#### anemone

##### MHB POTW Director
Staff member
Given the real numbers $a,\,b,\,c$ and $d$, prove that

$(1+ab)^2+(1+cd)^2+a^2c^2+b^2d^2\ge 1$

#### anemone

##### MHB POTW Director
Staff member
Expanding the LHS of the inequality we get $1+2ab+a^2b^2+1+2cd+c^2d^2+a^2c^2+b^2d^2=1+(1+ab+cd)^2+(ac-bd)^2\ge 1$