Question

If a+b+c = 10 ,
and a²+b²+c² = 36 , Find ab+bc+ca

Answer 1

Hey there!

Given,
( a + b + c) = 10

Also, a² + b² + c² = 36 .

So, Now ( a + b + c) = 10

Squaring on both sides.

( a + b + c) ² = 10²

( a ² + b² + c² )+ 2 ( ab + bc + ca) = 100

36 + 2 ( ab + bc + ca) = 100

2 ( ab + bc + ca) = 100 - 36

2 ( ab + bc + ca) = 64

( ab + bc + ca) = 64/2 = 32 .

Required answer is ( ab + bc + ca) = 32 .

Answer 2

Heya

We know :

${(a + b + c)}^{2} = ({a}^{2} + {b}^{2} + {c}^{2} + 2(ab + bc + ca))$

Now, we know about the values of :
$(a + b + c) = 10$
$( {a}^{2} + {b}^{2} + {c}^{2} ) = 36$
Filling these in the above Expansion :

${10}^{2} = (36 + 2(ab + bc + ca))$

$= > 100 = 36 + 2(ab + bc + ca)$

$= > (ab + bc + ca) = \frac{64}{2} = 32$

Hence, your desired value is :

( ab + bc + ca ) = 32

____________________________________

^_^ Hope it helps