Question

Find the value of 30+
(e) Ifa+b+c= 12 and a+b+c=64, find the value of ab + bc + ac.
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Answer 1

Step-by-step explanation:

(a+b+c) square = a square + b square + c square +2ab +2bc +2ca

(12) square = 64 + 2 ( ab + bc + ca)

144 = 64 + 2 ( ab + bc + ca)

144-64 = 2 ( ab + bc + ca)

80 = 2 ( ab +bc + ca)

80÷2 = ab + bc + Ca

40 = ab +bc +ca

Answer 2

We know a Algebraic Identity :

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

Substitute The Values

⇒ 12² = 64 + 2ab + 2bc + 2ac

⇒ 12² = 64 + 2(ab + bc + ac)

⇒ 144 = 64 + 2(ab + bc + ac)

Subtracting 64 from Both Sides

⇒ 144 - 64 = 64 + 2(ab + bc + ac) - 64

⇒ 80 = 2(ab + bc + ac)

Dividing Both Sides by 2

⇒ 80/2 = [2(ab + bc + ac)]/2

⇒ 40 = ab + bc + ac