Question

if a²+b²+c²=83 and a+b+c=15, then find the value of ab+bc+ca​

Answer 1

Answer:

a²+b²+c²+2(ab+bc+ca)= (a+b+c)²

83 + 2( ab+bc+ca) =(15)²

ab+bc+ca =(225-83)/2

=71

Answer 2

a^2 + b^2 + c^2 = 83 ------(1)

a + b+ c = 15

On squaring both sides, we get

a^2 + b^2 + c^2 + 2( ab + bc + ca) = 225

=> 83 + 2 ( ab + bc + ca) = 225

=> 2 ( ab + bc + ca) = 142

=> ab + bc + ca = 71 --------(2)

Now,

a^3 + b^3 + c^3 - 3abc = ( a +b + c) (a^2 + b^2 + c^2 - ab - bc - ca)

= ( 15) [ 83 - (ab + bc + ca)]

= (15)(83-71)

= 15 × 12

= 180