Question

If a + b + C is equal to 12 and a b + BC + CA is equal to 22 then find the value of a square + b square + c square ​

Answer 1

Given:

• a + b + c = 12
• ab + bc + ca = 22

To find: a² + b² + c² = ?

Solution:

We know that,

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

or, 12² = a² + b² + c² + 2 × 22

or, 144 = a² + b² + c² + 44

or, a² + b² + c² = 144 - 44

or, a² + b² + c² = 100

Answer: a² + b² + c² = 100

Answer 2

$\orange{\bigstar}$ Answer :

a² + b² + c² = 100

Given :

• a + b + c = 12
• ab + bc + ca = 22

To Find :

• a² + b² + c²

Solution :

a + b + c = 12

Squaring on both sides , we get ,

⇒ ( a + b + c )² = 12²

⇒ a² + b² + c² + 2ab + 2bc + 2ca = 144

⇒ a² + b² + c² + 2 ( ab + bc + ca ) = 144

⇒ a² + b² + c² + 2 ( 22 ) = 144 [ From given data ]

⇒ a² + b² + c² = 144 - 44

⇒ a² + b² + c² = 100

More Info :

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