Question

if a+b+c=6,a^2+b^2+c^2=34,then ab+bc+ca​

Answer 1

GIVEN :-

• a + b + c = 6.
• a² + b² + c² = 34.

TO FIND :-

• ab + bc + ca.

SOLUTION :-

As we know that ,

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

Substitute all the values,

➔ (6)² = 34 + 2(ab + bc + ca)

6² = 6 × 6 = 36,

➔ 36 = 34 + 2(ab + bc + ca).

Transpose 34 to L.H.S,

➔ 36 - 34 = 2(ab + bc + ca)

➔ 2 = 2(ab + bc + ca)

Transpose 2 to L.H.S ,

➔ 2/2 = ab + bc + ca

➔ ab + bc + ca = 1.

❑ Hence the required answer is 1.

ADDITIONAL INFORMATION :-

➳ ( x + y )² = x² + 2xy + y²

➳ ( x - y )² = x² - 2xy + y²

➳ ( x - y ) ( x -y ) = ( x - y )²

➳ ( x + y ) ( x + y ) = ( x + y )²

➳ x² - y² = ( x + y ) ( x - y )

Answer 2

Answer:

1

Step-by-step explanation:

a+b+c=6

a^2+b^2+c^2=34

36(6^2) =34+2(ab+bc+ca)

36-34=2(ab+bc+ca)

2=2(ab+bc+ca)

a=ab

a=aba÷a=b

2÷2=ab+bc+ca

1=ab+bc+ca