Question

If a + b + c = 7 and ab + bc + ca = 20, find the value of a 2 + b 2 + c 2.

Answer 1

(a+b+c)^2=(7)^2=49
a^2+b^2+c^2+(ab+bc+ca)=49
a^2+b^2+c^2+2(20)=49
a^2+b^2+c^2=49-40
so answer is 9

Answer 2

Given:

The value of a + b + c = 7 and ab + bc + ca = 20.

To Find:

The value of a² + b² + c² is?

Solution:

The given problem can be solved using algebraic expansions.

1. The values of  a + b + c is 7 and ab + bc + ca is 20.

2. Consider the algebraic from (a + b + c)²,

=> Expand the expression,

=>  ( a + b + c )² = a² + b² + c² + 2( ab + bc + ca ).

3. Substitute the values of a + b + c and ab + bc + ca in the above form,

=> (7)² = a² + b² + c² + 2( 20 ),

=> 49 = a² + b² + c² + 40,

=> 49 - 40 = a² + b² + c²,

=> a² + b² + c² = 9.

Therefore, the value of a² + b² + c² is 9.