If a + b + c = 9 and ab + bc + ca = 26, Find the value of


If $a+b+c=9$ and $a b+b c+c a=26$, Find the value of $a^{3}+b^{3}+c^{3}-3 a b c$



a + b + c = 9 and ab + bc + ca = 26

We know that,

$(a+b+c)^{2}=a^{2}+b^{2}+c^{2}+2(a b+b c+c a)$






we know that,

$a^{3}+b^{3}+c^{3}-3 a b c=(a+b+c)$

$\left(a^{2}+b^{2}+c^{2}-a b-b c-c a\right) a^{3}+b^{3}+c^{3}-3 a b c=(a+b+c)\left[\left(a^{2}+b^{2}+c^{2}\right)-(a b+b c+c a)\right] h e r e$


$a b+b c+c a=26$


$a^{3}+b^{3}+c^{3}-3 a b c=9[(29-26)]=9 * 3=27$

Hence, the value of $a^{3}+b^{3}+c^{3}-3 a b c$ is 27

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