If a + b = 11 and a 2 + b 2 = 65; find a 3 + b 3 .

By formula, ⇒ (a + b) 2 = a 2 + b 2 + 2ab ⇒ 11 2 = 65 + 2ab ⇒ 121 = 65 + 2ab ⇒ 2ab = 56 ⇒ ab = = 28. By formula, ⇒ (a + b) 3 = a 3 + b 3 + 3ab(a + b) ⇒ 11 3 = a 3 + b 3 + 3 × 28 × 11 ⇒ 1331 = a 3 + b 3 + 924 ⇒ a 3 + b 3 = 1331 - 924 = 407. Hence, a 3 + b 3 = 407.

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If a - 2b + 3c = 0; state the value of a³ - 8b³ + 27c³.

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If x + 5y = 10; find the value of x³ + 125y³ + 150xy - 1000.

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If x, y and z are three different numbers, then prove that :
x² + y² + z² - xy - yz - zx is always positive.

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Mathematics

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

Expansions

Related Questions

If a - 2b + 3c = 0; state the value of a³ - 8b³ + 27c³.

If x + 5y = 10; find the value of x³ + 125y³ + 150xy - 1000.

If x, y and z are three different numbers, then prove that :
x² + y² + z² - xy - yz - zx is always positive.

Mathematics

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

Expansions

Related Questions

If a - 2b + 3c = 0; state the value of a3 - 8b3 + 27c3.

If x + 5y = 10; find the value of x3 + 125y3 + 150xy - 1000.

If x, y and z are three different numbers, then prove that :x2 + y2 + z2 - xy - yz - zx is always positive.

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

If a - 2b + 3c = 0; state the value of a³ - 8b³ + 27c³.

If x + 5y = 10; find the value of x³ + 125y³ + 150xy - 1000.

If x, y and z are three different numbers, then prove that :
x² + y² + z² - xy - yz - zx is always positive.