Nilai dari 20223+120213−1=…

Pertanyaan

Nilai dari $fraction numerator 2021 cubed minus 1 over denominator 2022 cubed plus 1 end fraction equals horizontal ellipsis$

$\frac{2019}{2023}$
$\frac{2020}{2022}$
$\frac{2020}{2023}$
$\frac{2021}{2023}$
$\frac{2021}{2022}$

A. Hadiannur

Master Teacher

Mahasiswa/Alumni Universitas Gadjah Mada

Jawaban terverifikasi

Jawaban

jawaban yang benar adalah C.

Pembahasan

Ingat konsep :

$\begin{array}{rcl}\left(x+y\right)^2&=&x^2+y^2+2xy\\x^3-y^3&=&\left(x-y\right)\left(x^2+y^2+xy\right)\\x^3+y^3&=&\left(x+y\right)\left(x^2-y^2-xy\right)\\&&\end{array}$

Berdasarkan konsep identitas aljabar di atas diperoleh penyelesaiaan sebagai berikut :

$table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator 2021 cubed minus 1 over denominator 2022 cubed plus 1 end fraction end cell equals cell fraction numerator open parentheses 2021 minus 1 close parentheses open parentheses 2021 squared plus 2021 plus 1 squared close parentheses over denominator open parentheses 2022 plus 1 close parentheses open parentheses 2022 squared minus 2022 plus 1 squared close parentheses end fraction end cell row blank equals cell 2020 over 2023 cross times fraction numerator open parentheses 2021 squared plus 2022 close parentheses over denominator open parentheses open parentheses 2021 plus 1 close parentheses squared minus 2022 plus 1 close parentheses end fraction end cell row blank equals cell 2020 over 2023 cross times fraction numerator 2021 squared plus 2021 plus 1 over denominator 2021 squared plus 2 times 2021 plus 1 minus 2021 minus 1 plus 1 end fraction end cell row blank equals cell 2020 over 2023 cross times fraction numerator 2021 squared plus 2021 plus 1 over denominator 2021 squared plus 2021 plus 1 end fraction end cell row blank equals cell 2020 over 2023 end cell end table$

Oleh karena itu, jawaban yang benar adalah C.