If a+b+c=0 , then find the value of ..... (-2a)^3 + (-2b)^3 + (-2c)^3 - 3 (-2a)(-2b)(-2c)............. plzzzz answer me fast I will mark your answer as brainlist
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Answered by
7
Answer:
0
Step-by-step explanation:
Given Equation is (-2a)³ + (-2b)³ + (-2c)³ - 3(-2a)(-2b)(-2c)
Now,
∴ a³ + b³ + c³ - 3abc = (a + b + c)(a² + b² + c² - ab - bc - ca)
⇒ (-2a)³ + (-2b)³ + (-2c)³ - 3(-2a)(-2b)(-2c) = (0)[a² + b² + c² - ab - bc - ca]
⇒ (-2a)³ + (-2b)³ + (-2c)³ = 0.
Hope it helps!
Answered by
9
If a + b + c = 0, then
a = - ( b + c ), b = - ( a + c ) and c = - ( a + b )
Replacing the values in the question we obtain,
(-a)^2/bc + (-b)^2/ca + (-c)^2/ab
Now taking L.C.M
a^3 + b^3 + c^3 /abc
Using the identity,
If a +b +c = 0, then a^3 + b^3 + c^3 = 3abc
Hence, we get
3abc/abc = 3
Therefore , the value is 3.
a = - ( b + c ), b = - ( a + c ) and c = - ( a + b )
Replacing the values in the question we obtain,
(-a)^2/bc + (-b)^2/ca + (-c)^2/ab
Now taking L.C.M
a^3 + b^3 + c^3 /abc
Using the identity,
If a +b +c = 0, then a^3 + b^3 + c^3 = 3abc
Hence, we get
3abc/abc = 3
Therefore , the value is 3.
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