Question

If (a + b + c) = 12, ( ab+ bc+ ca)=47 then the value of a^2 + b^2+ c^2 is​

Answer 1

Answer:

Identity to be used here:

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

According to the question, it is given that:

→ ( a + b + c ) = 12

→ ( ab + bc + ac ) = 47

We are required to find the value of ( a² + b² + c² ).

Comparing the given information with the identity ( a + b + c )², we get:

→ ( 12 )² = a² + b² + c² + 2 ( 47 )

→ 144 = a² + b² + c² + 94

→ a² + b² + c² = 144 - 94

→ a² + b² + c² = 50

Hence the value of ( a² + b² + c² ) is 50.

Answer 2

Question:-

If (a + b + c) = 12, (ab+ bc+ ca) = 47 then the value of a² + b²+ c²

Formula Used:-

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

Answer:-

Given (a + b + c) = 12 and (ab+ bc+ ca) = 47, so putting the values in the formula,

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

➞ (12)² = a² + b² + c² + 2(47)

➞ 144 = a² + b² + c² + 94

➞ 144 - 94 = a² + b² + c²

➞ a² + b² + c² = 50

Ans. a² + b² + c² = 50