aligned & If x: y: z= ( 15 + ): ( 15 + ): & ( 15 + ), then z+x z-x ^2( - )+ x+y x-y & ^2( - )+ y+z y-z ^2( - )= aligned

Step-by-step solution

Given aligned & x: y: z= ( 15 + ): ( 15 + ): ( 15 + ) & x=k ( 15 + ), y=k ( 15 + ) & z=k ( 15 + ) aligned aligned & Now, z+x z-x ^2( - ) & = (12^ + )+ (12^ + ) (12^ + )- (12^ + ) ^2( - ) & = 24^ +( + ) ( - ) ^2( - ) & = [ 24^ ( + )+ 24^ ( + ) ] ( - ) & = array r 24^ [ ( + ) ( - )] + 24^ [ ( + ) ( - )] array aligned By adding Eqs. (i), (ii) and (iii), we get aligned & z+x z-x ^2( - )+ x+y x-y ^2( - ) & + y+z y-z ^2( - )=0 aligned