Question

Cho ba số a,b,c thỏa mãn: a¹⁰⁰+b¹⁰⁰=a¹⁰¹+b¹⁰¹=a¹⁰²+b¹⁰²

Tính P=a²⁰¹⁰+b²⁰¹⁰

Answer 1

\(\left(a^{100}+b^{100}\right)ab-\left(a^{101}+b^{101}\right)\left(a+b\right)+a^{102}+b^{102}=a^{101}b+b^{101}a-a^{102}-b^{102}-a^{101}b-b^{101}a+a^{102}+b^{102}=0\Rightarrow\left(a^{102}+b^{102}\right)\left(ab-a-b+1\right)=0\Leftrightarrow\left(a^{102}+b^{102}\right)\left(a-1\right)\left(b-1\right)=0\) \(\Leftrightarrow\left[{}\begin{matrix}a^{102}+b^{102}=0\\a-1=0\\b-1=0\end{matrix}\right.\)

\(+,a^{102}+b^{102}=0\Rightarrow P=0\)

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