Question

If a+b+c=9,and ab+bc+ca=40, find a²+b²+c²​

Answer 1

Answer:

1

Step-by-step explanation:

We know,

(a+b+c)

2

=a

2

+b

2

+c

2

+2(ab+bc+ca)

9

2

=a

2

+b

2

+c

2

+2×40

81=a

2

+b

2

+c

2

+80

a

2

+b

2

+c

2

=1

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Answer 2

Given :-

• Value of a + b + c = 9.
• Value of ab + bc + ca = 40.

To Find :-

• The value of a² + b² + c².

Solution :-

As we know that,

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

[ Putting values ]

↪(9)² = a² + b² + c² + 2(ab + bc + ac)

↪81 = a² + b² + c² + 2(40)

↪81 = a² + b² + c² + 80

↪a² + b² + c² = 81 - 80

↪a² + b² + c² = 1

Hence,

• The value of a² + b² + c² is 1.

______________

☀ Verification ☀

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

[ Putting values ]

↪(9)² = 1 + 2(ab + bc + ac)

↪81 = 1 + 2(40)

↪81 = 1 + 80

↪81 = 81

Hence verified!!