Question

if a+b+ c = 7 and ab+ bc+ ca= 2a find the
value of a^2 + b^2 + c^2
use (a+b+c) ² = a² + b² + c² + [2 (ab + bc + ca]​

Answer 1

Refer the attachment for your answer...

Answer 2

Solution :-

Given ,

• a + b + c = 7
• ab + bc + ac = 2a
• Hint :- ( a + b + c )² = a² + b² + c² [ 2 ( ab + bc + ac ) ]

We need to find ,

• a² + b² + c²

By using the given hint ,

• ( a + b + c )² = a² + b² + c² + [ 2 ( ab + bc + ac ) ]

Substituting the given values

⇒ ( 7 ) ² = a² + b² + c² + [ 2 ( 2a ) ]

⇒ 7² = a² + b² + c² + [ 4a ]

⇒ 49 = a² + b² + c² + 4a

⇒ 49 - 4a = a² + b² + c²

[ °.° 4 transposed to RHS ]

⇒ a² + b² + c² = 49 - 4a

Hence , a² + b² + c² = 49 - 4a