If a + B = 11 and A2 + B2 = 65; Find A3 + B3. - Mathematics

If a + b = 11 and a² + b² = 65; find a³ + b³.

Sum

a + b = 11 and a2 + b2 = 65
Now, (a+b)² = a² + b² + 2ab
⇒ (11)² = 65 + 2ab
⇒ 121 = 65 + 2ab
⇒ 2ab = 56
⇒ ab = 28

a³ + b³ = ( a + b )( a² - ab + b2)
= (11)(65 - 28)
= 11 x 37
= 407

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Chapter 4: Expansions (Including Substitution) - Exercise 4 (E) [Page 66]

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