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

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

If `"a"^2+ 1/"a"^2=23`, find : `"a" +1/"a"`

If a + b + c = 10 and a² + b² + c² = 38, find : ab + bc + ca

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

Find : a + b + c, if a² + b² + c² = 83 and ab + bc + ca = 71.

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

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

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

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