Question

If a + b + c = 7 and $a^3 + b^3 + c^3-3abc = 175$, then what is the value of (ab + bc + ca)?

• A. 8
• B. 7
• C. 6
• D. 9

Answer 1

Answer:

A. 8

Solution:

Given:

a + b + c = 7

a³ + b³ + c³ - 3abc = 175

Concept used:

a³ + b³ + c³ - 3abc = (a + b + c)[(a + b + c)² - 3(ab + bc + ca)]

Calculation:

$a^3+b^3+c^3-3abc=(a+b+c)[(a+b+c)^2-3(ab+bc+ca)]$

⇒$175=7\times{[(7)^2-3(ab+bc+ca)]}$

⇒$25=49-3(ab+bc+ca)$

⇒ 24 = 3(ab + bc + ca)

⇒ ab + bc + ca = 8

∴ The value of given identities is 8.