(root-3root-b) is equal to
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Answer:
Answer:
(a+b+c)^3=27abc(a+b+c)
3
=27abc
Step-by-step explanation:
Formula used:
if x+y+z=0 then x^3+y^3+z^3=3xyzx
3
+y
3
+z
3
=3xyz
Given:
\sqrt[3]{a}+\sqrt[3]{b}+\sqrt[3]{c}=0
3
a
+
3
b
+
3
c
=0
From the above formula
(\sqrt[3]{a})^3+(\sqrt[3]{b})^3+(\sqrt[3]{c})^3=3\sqrt[3]{a}\sqrt[3]{b}\sqrt[3]{c}(
3
a
)
3
+(
3
b
)
3
+(
3
c
)
3
=3
3
a
3
b
3
c
a+b+c=3\sqrt[3]{a}\sqrt[3]{b}\sqrt[3]{c}a+b+c=3
3
a
3
b
3
c
Now,
(a+b+c)^3=(3\sqrt[3]{a}\sqrt[3]{b}\sqrt[3]{c})^3(a+b+c)
3
=(3
3
a
3
b
3
c
)
3
(a+b+c)^3=3^3(\sqrt[3]{a})^3(\sqrt[3]{b})^3(\sqrt[3]{c})^3(a+b+c)
3
=3
3
(
3
a
)
3
(
3
b
)
3
(
3
c
)
3
(a+b+c)^3=27abc(a+b+c)
3
=27abc
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