Question

If a+b+ c =9 and ab + bc + ca = 23, then a²+b² + c²=
A. 35
B. 58
B. 127
D. none of these

Answer 1

Given : a + b + c = 9 and ab + bc + ca = 23

By using an algebraic identity :  

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

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

(9)² = a² + b² + c² + 2(23)

81 = a² + b² + c² + 46

a² + b² + c²  = 81 - 46

a² + b² + c² = 35

Hence, the value of a² + b² + c² is 35.

Option (A) 35 is correct.

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Answer 2

Answer:

Step-by-step explanation:

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

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

(9)² = a² + b² + c² + 2(23)

81 = a² + b² + c² + 46

a² + b² + c²  = 81 - 46

a² + b² + c² = 35