Question

if a + b + c equal to a and a square + b square + c square equals to 35 find the value of a cube plus b cube plus c cube - 3abc​

Answer 1

Answer:

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Step-by-step explanation:

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Answer 2

${\fbox{\boxed {\huge{\rm{\red{Answer!!}}}}}}$

Given:-

${\rm{(a + b + c) \: and \: ( {a }^{2} + {b}^{2} + {c}^{2} = 35)}}$

${\rm{Considerd(a + b + c) = 9}}$

Squaring on the both side , We will get

${\rm{\implies({ a + b + c})^{2} = 92}}}$

${\rm{\implies{ {(a + b + c})^{2} = {a}^{2} + {b}^{2} + {c}^{2} + 2(ab + bc + ca)}}}$

${\rm {\implies{{a}^{2} + {b}^{2} + {c}^{2} + 2(ab + bc + ca) = 81}}}$

${\rm {\implies{35 + 2(ab + bc + ca) = 81}}}$

${\rm {\implies{ 2(ab + bc + ca) = 81 - 35 = 46}}}$

${\rm {\implies{ 2(ab + bc + ca) = \frac{46}{2} }}}$

${\boxed{\rm { { \therefore 2(ab + bc + ca) = 23 }}}}$

Now, We have

${ \implies {\rm{{a}^{3} + {b}^{3} + {c}^{3} - 3abc = (a + b + c)}}}$

${\rm{ ({a}^{2} + {b}^{2} + {c}^{2} - ab - bc - ca)}}$

${\implies{\rm{(a + b + c)({a}^{2} + {b}^{2} + {c}^{2} - (ab + bc + ca))}}}</p><p>$

${ \implies{\rm{9(35 - 23)}}} \\ { \implies{\rm{9 \times 12)}}}$

${\red {\green{\fbox{\boxed{ \implies{\rm{108}}}}}}}$