Question

If a+b+c= 3, a²+b²+c²=5,a³+b³+c³=9 find the value of abc

Answer 1

Answer:

abc = 2

Step-by-step explanation:

(a + b + c) = 3

(a + b + c)² = 3²

a² + b² + c² +2(ab + bc + ca) = 9

5 + 2(ab + bc + ca) = 9

2(ab + bc + ca) = 9 - 5

2(ab + bc + ca) = 4

(ab + bc + ca) = 4/2

(ab + bc + ca) = 2

(a + b + c) = 3

(a² + b² + c²) = 5

(ab + bc + ca) = 2

(a³ + b³ + c³) = 9

Subtract 3abc from both sides.

a³ + b³ + c³ - 3abc = 9 - 3abc

(a + b + c)[a² + b² + c² - (ab + bc + ca)] = 9 - 3abc

(3)(5 - 4) = 9 - 3abc

3 × 1 = 9 - 3abc

3 = 9 - 3abc

3abc = 9 - 3

3abc = 6

abc = 6/3

abc = 2

Hope this helps

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