Question

If a = 299, b = 298, c = 297 then the value of 2a³ + 2b³ + 2c³ – 6abc is:

• A. 5152
• B. 5267
• C. 5364
• D. 5456

Answer 1

Answer:

C. 5364

Solution:

Given:

a = 299

b = 298

c = 297

Formula used:

[a³ + b³ + c³ – 3abc] = $\frac{1}{2}\times$ (a + b + c)[(a – b)² + (b – c)² + (c – a)²]

Calculation:

2a³ + 2b³ + 2c³ – 6abc

= 2[a³ + b³ + c³ – 3abc]

= $2\times{\frac{1}{2}}\times$ (a + b + c)[(a – b)² + (b – c)² + (c – a)²]

= (299 + 298 + 297) [(299 – 298)² + (298 – 297)² + (297 – 299)²]

= 894 [1² + 1² + 2²]

= $894 \times{6}$

= 5364