Let a, b, c ∈R be such that $$a+b+c$$$$0$$ and $$abc=2$$. Let $$A=a$$ b cb c ac a b If $$A2=I$$, then value of $$a3+b3+c3$$ is

Question

Let a, b, c ∈R be such that $$a+b+c$$>$$0$$ and $$abc=2$$. Let $$A=a$$    b    cb    c    ac    a    b If $$A2=I$$, then value of $$a3+b3+c3$$ is

Infinity Learn · Accepted Answer

$$A2=a$$    b    cb    c    ac    a    ba    b    cb    c    ac    a    $$b=$$αβββαβββαwhere α$$=a2+b2+c2$$,          β$$=bc+ca+ab$$.As $$A2=I$$, we $$geta2+b2+c2=$$α$$=1bc+ca+ab=0Now$$, $$(a+b+c)2=$$α$$+2$$β$$=1$$⇒  $$a+b+c=1We$$ have $$a3+b3+c3$$−$$3abc=(a+b+c)a2+b2+c2$$−bc−ca−$$ab=1$$⇒$$a3+b3+c3=7$$

Let $a, b, c \in R$ be such that $a + b + c > 0$ and $a b c = 2 .$ Let $A = [\begin{array}{lll} a b c \\ b c a \\ c a b \end{array}]$ If $A^{2} = I,$ then value of $a^{3} + b^{3} + c^{3}$ is

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Let a, b, c ∈R be such that a+b+c>0 and abc=2. Let A=a b cb c ac a b If A2=I, then value of a3+b3+c3 is

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Let $a, b, c \in R$ be such that $a + b + c > 0$ and $a b c = 2 .$ Let $A = [\begin{array}{lll} a b c \\ b c a \\ c a b \end{array}]$ If $A^{2} = I,$ then value of $a^{3} + b^{3} + c^{3}$ is