Question

(a) If a+b+c=9, a2 + b2 + c2 = 51, find ab + bc + ca​

Answer 1

Answer:

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Step-by-step explanation:

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

∴ (9)2 = a2 + b2 + c2 + 2(15)

81 = a2 + b2 + c2 + 30

∴ a2 + b2 + c2 = 81 – 30 = 51

Answer 2

The value of (ab+ bc+ ca) = 15

Given:

If  a + b + c = 9 and  a² + b² + c² = 51

To find:

Find  the value of  (ab + bc + ca​)

Solution:

Given that a + b + c = 9 and  a² + b² + c² = 51

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

⇒ (9)² = 51 + 2(ab + bc + ca)

⇒  81 = 51 + 2(ab + bc + ca)    [ ∵ 9² = 81 ]

⇒ 2(ab + bc + ca) = 81 - 51

⇒ 2(ab + bc + ca) = 30

⇒ ab + bc + ca = 15

Therefore, the value of (ab+ bc+ ca) = 15

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