If a + b + c =5, a² + b ² + c ² = 37
and a3 + b3 + c3 = 125 then the value
of 4abc is -
Answers
Answer: 4abc = -20
Step-by-step explanation:
Given data
a+b+c = 5
a²+ b² + c² = 27
a³ + b³ + C³ = 125
To find - 4 abc
(a+b+c)² = a² + b² + c² + 2ab + 2bc +2ca ------------> 1
Substitute the values of (a+b+c) and a²+b²+c² in the equation 1
(5)² = 27 + 2(ab + bc+ ca)
25 = 27 + 2(ab + bc+ ca)
-2 = 2(ab + bc+ ca)
Eliminate 2 on both sides of the equation
(ab + bc+ ca) = -1 -------------->2
(a³ + b³ +c³) = (a+b+c)(a² + b² +c² -ab -bc-ca) ------------>3
Substitute a+b+c = 5, a²+ b² + c² = 27, a³ + b³ + C³ = 125 in the above equation
(125- 3abc) = 5 (27 - ( -1))
(125- 3abc) = 135 + 5
(125- 3abc) = 140
-3abc = 15
abc = - 5
Multiply 4 on the both sides of the above equation
4 abc = 4× (-5)
4 abc = -20
Answer:
Step-by-step explanation:
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