Question

if a + b + C is equal to 2 and a square + b square + b square equal to 64 find the value of a b + BC + AC

Answer 1

Hello,


We know the algebraic identity that :-

${(a + b + c)}^{2} = {a}^{2} + {b}^{2} + {c}^{2} + 2(ab + bc + ca)$
${(2)}^{2} = 64 + 2(ab + bc + ca) \\ \\ 64 + 2(ab + bc + ca ) = 4 \\ \\ 2(ab + bc + ca) = 4 - 64 = ( - 60) \\ \\ ab + bc + ca = \frac{( - 60)}{2} = ( - 30)$

So,

Putting the values of
A+B+C =2

And
A²+B²+C² = 64

AB+BC+CA =??

so
Putting the values in the formula mentioned above :-

We get the answer as (-30)


Hope this will be helping you.....