Question

If a-b=3 and b-c=5 then the value of a square+b square +c square - ab-bc-ca is

Answer 1

A - b = 3 and b - c = 5 then a²+b²+c² - ab - bc - ca= ?

a-b= 3⇒ a= 3+b ··· (1)
b-c =5 ⇒ b= 5+c ···(2)
From (1) and (2) we get, 
a = 3+5+c = 8+c •••(3)
Now, 
a + b + c - ab - bc - ca = 
(8+c)²+(5+c)²+c² -(8+c)(5+c) - (5+c)(c) -(c)(8+c)
=(64 + 16c +c²) + (25 + 10c + c²) + c² -(40+8c+5c+c²) - (5c+c²) - (8c+c²)
=(64+25+ 26c + 3c²) - (40+26c+3c²)
=(89 - 40)+ (26c -26c) + (3c² - 3c²)
=89 - 40 =49