Question

If 3 3 3 a b c 0

   then (a + b + c)3

=




with explanation​

Answer 1

Step-by-step explanation:

FORMULA USED:

If X + y + z = 0 then x³ + y³ + z³ = 3xyz

Given:

$\sqrt[3]{a} + \sqrt[3]{b} + \sqrt[3]{c} = 0 \: \: then \: \\ {( \sqrt[3]{a} )}^{3} + {( \sqrt[3]{b} )}^{3} + {( \sqrt[3]{c}) }^{3} = 3 \sqrt[3]{a} \sqrt[3]{b} \sqrt[3]{c} \\ \\ now </u></strong><strong><u>,</u></strong><strong><u>\: a + b + c = 3 \sqrt[3]{a} \sqrt[3]{b} \sqrt[3]{c} \\ \\ cubing \: both \: sides </u></strong><strong><u>,</u></strong><strong><u> \\ {(a + b + c)}^{3} = {(3 \sqrt[3]{a} \sqrt[3]{b} \sqrt[3]{c} ) }^{3} \\ {(a + b + c)}^{3} = {(3)}^{3} \times {( \sqrt[3]{a}) }^{3} \times {( \sqrt[3]{b} )}^{3} \times {( \sqrt[3]{c}) }^{3} \\ {(a + b + c)}^{3} = 27abc$

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