Question

if a + b + c = 6 ab + bc + ca = 11 find a²+b²+c²​

Answer 1

Answer:

(a+b+c)^2 = a^2 + b^2 + c^2 + 2(ab+bc+ca)

6^2 = a^2 + b^2 + c^2 + 2*11

a^2 + b^2 + c^2 = 36 - 22

= 14

Answer 2

GIVEN :-

• a + b + c = 6.
• ab + bc + ca = 11.

TO FIND :-

• The value of a² + b² + c².

SOLUTION :-

We know that,

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

• [ substitute all the given values ]

→ (6)² = a² + b² + c² + 2(11)

→ 6 × 6 = a² + b² + c² + 2 × 11

→ 36 = a² + b² + c² + 22

→ 36 - 22 = a² + b² + c²

→ a² + b² + c² = 14.

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 )

➳ ( x + y + z )² = x² + y² + z² + 2xy + 2yz + 2zx.

➳ ( x + a ) ( x + b ) = x² + ( a + b)x + ab