Решаю уравнение :

( х – 3 )² + ( х – 5 )² = 25 ;

( х – 3 )² + ( х – 5 )² – 25 = 0 ;

х² – 6х + 9 + х² – 10х + 25 – 25 = 0 ;

2х² – 16х + 9 = 0 ;

а = 2 ; b = – 16 ; c = 9 ;

D = b² – 4ac = ( – 16 )² – 4 · 2 · 9 = 256 – 72 = 184 ;

x_(1) = ( – b – √D ) / ( 2a ) = (–(–16–√184))/(2·2) = (16–2√46)/4 = (2(8–√46))/4 = (8–√46)/2 ;

x_(2) = (–b+√D)/(2a)=(–(–16+√184))/(2*2)=(16+2√46)/4=(2(8+√46))/4=(8+√46)/2.

Ответ :