Question

12) If a + b = - 1 , then the value of a ^ 3 + b ^ 3 - 3ab is a) 26 C) -1 b) 1 d) -26​

Answer 1

Answer:

Option (c) is correct.

a + b = -1 (Given)

We know that,

(a + b)³ = a³ + b³ + 3ab(a + b)

⇒ (a + b)³ = (-1)³

⇒ a³ + b³ + 3ab(a + b) = (-1)³

⇒a³ + b³ + 3ab(-1) = -1

⇒a³ + b³ - 3ab = -1

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More algebraic identities:

• (a + b)² = a² + 2ab+ b²
• (a - b)² = a² - 2ab+ b²
• a² - b² = (a + b)(a - b)
• (a + b + c)² = a² + b² + c² + 2ab + 2bc + 2ca
• (a + b)³ = a³ + b³ + 3ab(a + b)
• (a - b)³ = a³ - b³ - 3ab(a - b)
• a³ - b³ - 3abc = (a + b + c)(a² + b² + c² -ab -bc -ca)
• (x + a)(x + b) = x² + (a + b)x + ab

Answer 2

Step-by-step explanation:

We know that (a−b)

3

=a

3

−b

3

−3ab(a−b)

Given that

a−b=1

Cubing on both sides, we get

⇒(a−b)

3

=a

3

−b

3

−3ab(a−b)

Substituting the value of a−b we get,

⇒(1)

3

=a

3

−b

3

−3ab(1)

Therefore, ⇒a

3

−b

3

−3ab=1