Question

a² + b ² + c ² = 50, ab + bc + ca= 47. Then a+b+c=?​

Answer 1

Given

• a² + b² + c² = 50
• ab + bc + ca = 47

To find

• a + b + c = ?

Solution

By algebraic identity we know,

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

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

putting known values

⇨ ( a + b + c )² = ( 50 ) + 2 ( 47 )

⇨ ( a + b + c )² = 144

⇨ a + b + c = √(144) = 12

therefore,

a + b + c = 12     ( Ans. )

_______________________

◈ More algebraic identities to know

◾ (a + b)² = a² + b² + 2 ab

◾ (a - b)² = a² + b² - 2 ab

◾ a² - b² = ( a + b ) ( a - b )

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

◾ (x + y)³ = x³ + y³ + 3 xy ( x + y )

◾ (x - y)³ = x³ - y³ - 3 xy ( x - y )

_______________________