Where's the most important substitution?

Algebra Level 3

(7+43)x25x+5+(743)x25x+5=14\large { (7+4\sqrt { 3 } ) }^{ { x }^{ 2 }-5x+5 }+{ (7-4\sqrt { 3 } ) }^{ { x }^{ 2 }-5x+5 }=14

Suppose a 4-digit number ABCD\overline{ABCD} with A<B<C<DA<B<C<D and all its 4 digits satisfy the equation above.

Determine the value of ABCD\overline{ABCD}.

×

Problem Loading...

Note Loading...

Set Loading...