Question

If a+b+c= 0 and a²+b² + c² = 16 then find ab+bc + ca​

Answer 1

Answer:

a + b + c =0

a² +b² +c² = 16

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

0² = 16 +2(ab +bc+ca)

0 = 16 +2(ab +bc+ca)

-16 = 2(ab+ bc +ca)

-8 = ab + bc + ca

SO UR ANSWER IS -8

PLEASE MARK MY ANSWER AS BRAINLIEST ✌

Answer 2

ANSWER:

• The value of ab+bc+ca = (-8)

GIVEN:

• a+b+c= 0
• a²+b² + c² = 16 .....(i)

TO FIND:

• ab+bc + ca

SOLUTION:

=> a+b+c=0

Squaring both sides we get;

=> (a+b+c)²= (0)²

=> a²+b²+c²+2ab+2bc+2ca = 0

=>(a²+b²+c²)+2(ab+bc+ca) = 0

Putting (a²+b²+c²) = 16 from eq (i) we get

=> 16 +2(ab+bc+ca)= 0

=> 2(ab+bc+ca)=(-16)

=> (ab+bc+ca) = (-16)/2

=> (ab+bc+ca) = (-8)

The value of ab+bc+ca = (-8)

NOTE:

some important formulas:

• (a+b)²= a²+b²+2ab
• (a-b)²= a²+b²-2ab
• (a+b+c)²= a²+b²+c²+2ab+2bc+2ca
• (a+b)³ = a³+b³+3ab(a+b)
• (a-b)³ = a³-b³-3ab(a-b)