Question

Find the value of ab+bc+ca, if a+b+c=9 and a2+b2+c2=35

Answer 1

a+b+c=9and a2+b2+c2=35 then by using identity
(a+b+c)2=a2+b2+c2+2ab+2bc+2ca,weget the answer (9)2=35+2(ab+BC+CA
2(ab+BC+CA)=(9)2-35
2(ab+BC+CA) =81-35then we get ab+BC+CA=46/2 so ab+BC+CA=23

Answer 2

The value of ab + bc + ca = 23

Given :

a + b + c = 9 and a² + b² + c² = 35

To find :

The value of ab + bc + ca

Formula :

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

Solution :

Step 1 of 2 :

Write down the given data

Here it is given that

a + b + c = 9 and a² + b² + c² = 35

Step 2 of 2 :

Find the value of ab + bc + ca

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

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

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

⇒ 2(ab + bc + ca) = (9)² - 35

⇒ 2(ab + bc + ca) = 81 - 35

⇒ 2(ab + bc + ca) = 46

⇒ ab + bc + ca = 46/2

⇒ ab + bc + ca = 23

Hence the value of ab + bc + ca = 23

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