If (11a 2 + 13b 2 )(11c 2 - 13d 2 ) = (11a 2 - 13b 2 )(11c 2 + 13d 2 ), prove that a : b : : c : d.

Given, (11a 2 + 13b 2 )(11c 2 - 13d 2 ) = (11a 2 - 13b 2 )(11c 2 + 13d 2 ). On cross-multiplication, By componendo and dividendo, On dividing the equation by , Hence, proved that a, b, c, d are in proportion.