Question

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Answer 1

Answer:

The answer is 495.

Step-by-step explanation:

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Answer 2

Question :

If a + b + c = 9 and ab + bc + ca = 26, then the value of a³ + b³ + c³ - 3abc is :

• 27
• 29
• 495
• 729

Answer :

If a + b + c = 9 and ab + bc + ca = 26, then the value of a³ + b³ + c³ - 3abc is 27.

Explanation :

Given :

• a + b + c = 9
• ab + bc + ca = 26

To Find :

• a³ + b³ + c³ - 3abc = ?

Solution :

We know that :

• $\underline{\boxed{\bf{a^{3} + b^{3} + c^{3} - 3abc = ( a + b + c)(a^{2} + b^{2} + c^{2} - ab - bc - ca)}}}$

$\sf : \implies a^{3} + b^{3} + c^{3} - 3abc = ( a + b + c)(a^{2} + b^{2} + c^{2} - ab - bc - ca)$

Now, we know that :

• $\underline{\boxed{\bf{a^{2} + b^{2} + c^{2} = (a+b+c)^{2} - 2ab - 2bc - 2ca}}}$

$\sf : \implies a^{3} + b^{3} + c^{3} - 3abc = [ a + b + c][(a+b+c)^{2} - 2ab - 2bc - 2ca - ab - bc - ca]$

$\sf : \implies a^{3} + b^{3} + c^{3} - 3abc = [a + b + c][(a+b+c)^{2} - 3ab - 3bc - 3ca]$

$\sf : \implies a^{3} + b^{3} + c^{3} - 3abc = [ a + b + c][(a+b+c)^{2} - 3(ab + bc + ca)]$

Now, we have :

• a + b + c = 9
• ab + bc + ca = 26

By filling values :

$\sf : \implies a^{3} + b^{3} + c^{3} - 3abc = [9][(9)^{2} - 3(26)]$

$\sf : \implies a^{3} + b^{3} + c^{3} - 3abc = (9)(81 - 78)$

$\sf : \implies a^{3} + b^{3} + c^{3} - 3abc = (9)(3)$

$\sf : \implies a^{3} + b^{3} + c^{3} - 3abc = 9 \times 3$

$\sf : \implies a^{3} + b^{3} + c^{3} - 3abc = 27$

Hence, value of a³ + b³ + c³ - 3abc is 27.