Question

If a-b = 3 ,b-c=5 then find the value of a×a+b×b+c×c-ab-bc-ca

Answer 1

hello users ......

we have given that 
a - b = 3 ...........(1) 
and
b - c = 5 .................(2)

we have to find 
 a² + b² + c² -ab - bc - ca = ?

solution:-
now adding  (1) and (2) ,we get
a - c = 3 +5 = 8 ...........(3)

now,
squaring and adding (1) ,(2) and (3)

we get ,

 (a - b)² + ( b - c)² + (a - c)² = 3²  + 5²  + 8² 
=  (a² + b² - 2ab ) +(b² + c² - 2bc) + ( a² + c² - 2ac) = 9 + 25 + 64

= 2a² +2b² +2c² -2ab - 2bc - 2ac = 98

= 2(a² +b² +c² -ab - bc - ac) = 2 × 49

=> (a² +b² +c² -ab - bc - ac) = 49 answer 

⭐⭐hope it helps ⭐⭐