If A+B=5 and Ab = 6, Find A2 + B2

If a+b=5 and ab = 6, find a² + b²

Sum

(a + b)² = a²+ b² + 2ab

⇒ (5)² = a² + b²+ 2×6

⇒ 25 = a² + b² + 12

⇒ 25 − 12 = a² + b²

⇒ 13 = a² + b²

∴ a² + b² = 13

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Application of Formulae

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Chapter 12: Identities - Exercise 12 (C) [Page 154]

Chapter 12 Identities
Exercise 12 (C) | Q 1 | Page 154

If a – b = 6 and ab = 16, find a² + b²

If a² + b² = 29 and ab = 10, find : a + b

If a² + b² = 29 and ab = 10, find : a − b

If `"a" - 1/"a"=4`, find : `"a"^2+1/"a"^2`

Find: a² + b² + c², if a + b + c = 9 and ab + bc + ca = 24

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