Question

If a+b+c=10 and a2+b2+c2=38 find ab+bc+ca​

Answer 1

Answer:

$\huge\boxed{\fcolorbox{lime}{Pink}{HEYA YOUR ANSWER IS HERE⚡}}$

Step-by-step explanation:

a + b + c = 10

⇒ (a + b + c)2 = (10)2

⇒ a2 + b2 + c2 + 2ab + 2bc + 2ca = 100

⇒ 38 + 2(ab + bc + ca) = 100

⇒ 2(ab + bc + ca) = 62

⇒ 2(ab + bc + ca) = 62

⇒ (ab + bc + ca) = 62/2

⇒ ab + bc + ca = 31

Alternative Method

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

⇒ (10)2 = 38 + 2(ab + bc + ca)

⇒ 100 = 38 + 2(ab + bc + ca)

⇒ 100 - 38 + 2(ab + bc + ca)

⇒ 62 = 2(ab + bc + ca)

⇒ 62/2 = ab + bc + ca

⇒ 31 = ab + bc + ca

HEYA FRIEND HAVE A GOOD DAY

∴ ab + bc + ca = 31

Answer 2

Answer:

31

Step-by-step explanation:

Given,

a + b + c = 10

a² + b² + c² = 38

To find : ab + bc + ca = ?

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

Identity

10² = 38 + 2 ( ab + bc + ca )

100 = 38 + 2 ( ab + bc + ca )

100 - 38 = 2 ( ab + bc + ca )

2 ( ab + bc + ca ) = 62

ab + bc + ca = 62 / 2

ab + bc + ca = 31