Question

if a+b+c=9 and ab+bc+ca=23,find the value of
$a {}^{2} + b { }^{2} + c {}^{2}$
​

Answer 1

Answer :-

Given :-

• a + b + c = 9
• ab + bc + ca = 23

To Find :-

• a² + b² + c²

Solution :-

Using the identity :-

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

Substituting the values :-

→ 9² = a² + b² + c² + 2 × 23

→ 81 = a² + b² + c² + 46

→ a² + b² + c² = 81 - 46

→ a² + b² + c² = 35

Value of a² + b² + c² is 35.

Additional Information -

(a + b)² = a² + 2ab + b²

(a - b)² = a² - 2ab + b²

a² + b² = (a + b)² - 2ab

a² + b² = (a - b)² + 2ab

(a + b)³ = a³ + 3a²b + 3ab² b³

(a + b)³ = a³ + b³ + 3ab(a + b)

(a - b)³ = a³ - 3a²b + 3ab² - b³

a³ + b³ = (a + b)( a² - ab + b² )

a³ + b³ = (a + b)³ - 3ab( a + b)

a³ - b³ = (a - b)( a² + ab + b²)

a³ - b³ = (a - b)³ + 3ab ( a - b )