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

If `"a"^2+ 1/"a"^2=11`, find : `"a" -1/"a"`

If a + b = 6 and ab = 8, find: a³ + b³.

Find : `"a"^3+1/"a"^3`, if `"a" +1/"a"=5`.

If `2"x"-1/(2"x")=4`, find: `8"x"^3-1/(8"x"^3)`

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)`

If a² + b² = 41 and ab = 4, find : a – b

If 3x + 2y = 9 and xy = 3, find : 27x³ + 8y³.

The difference between the two numbers is 5 and their products are 14. Find the difference between their cubes.