Question

if asquare + bsquare +csquare =20 and a+b+c=0,find ab+bc+ca​

Answer 1

Answer:

Value of (ab + bc + ca ) is (-10)

Given

• a² + b² + c² = 20
• ( a + b + c ) = 0

To Find:

• ab + bc + ca

Identity:

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

Substituting value of ( a + b + c ) and ( a² + b² + c² )

➞ ( 0 )² = 20 + 2(ab + bc + ca )

➞ 0 = 20 + 2(ab + bc + ca )

➞ -20 = 2(ab + bc + ca )

➞ -20/2 = (ab + bc + ca )

➞ -10 = (ab + bc + ca )

Value of (ab + bc + ca ) is (-10)

Verification:

➞ (0)² = 20 + 2 ( -10 )

➞ 0 = 20 + ( -20 )

➞ 0 = 0

LHS = RHS

Verified.

Answer 2

( a+ b + c) 2 = a2 + b2 + c2 + 2

( ab + bc + ac )

ab + bc + ac

= -20 / 2

= -10