If a + B + C = 11 and A2 + B2 + C2 = 81, Find : Ab + Bc + Ca.

If a + b + c = 11 and a² + b² + c² = 81, find : ab + bc + ca.

Sum

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

∴ (11)² = 81 + 2 (ab + bc + ca)

∴ 2(ab + bc + ca) = 121 − 81 = 40

ab + bc + ca = `40/2`

⇒ ab + bc + ca = 20

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Application of Formulae

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Chapter 12: Identities - Exercise 12 (D) [Page 155]

Chapter 12 Identities
Exercise 12 (D) | Q 11 | Page 155

If a² + b²= 10 and ab = 3; find : a – b

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If `3"x"+1/(3"x")=3`, find : `9"x"^2+1/(9"x"^2)`

If `3"x"+1/(3"x")=3`, find : `27"x"^3+1/(27"x"^3)`

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(i) the sum of the two numbers.
(ii) the difference between them.

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If 5x – 4y = 7 and xy = 8, find : 125x³ – 64y³.