Aljabar

Sifat-Sifat Aljabar

\left(x+\dfrac1x\right)^2=x^2+\dfrac1{x^2}+2
x^2+\dfrac1{x^2}=\left(x+\dfrac1x\right)^2-2

\begin{aligned} \left(x+\dfrac1x\right)^2&=x^2+2(x)\left(\dfrac1x\right)+\left(\dfrac1x\right)^2\\[6pt] &=x^2+2+\dfrac1{x^2}\\[6pt] &=x^2+\dfrac1{x^2}+2 \end{aligned}

\left(x+\dfrac1x\right)^2=x^2+\dfrac1{x^2}+2
x^2+\dfrac1{x^2}=\left(x+\dfrac1x\right)^2-2

\begin{aligned} \left(x+\dfrac1x\right)^2&=x^2+2(x)\left(\dfrac1x\right)+\left(\dfrac1x\right)^2\\[6pt] &=x^2+2+\dfrac1{x^2}\\[6pt] &=x^2+\dfrac1{x^2}+2 \end{aligned}

RUMUS-RUMUS PENTING

\left(a+\dfrac1b\right)\left(b+\dfrac1c\right)\left(c+\dfrac1a\right)=a+\dfrac1b+b+\dfrac1c+c+\dfrac1a+abc+\dfrac1{abc}

a,b,c\neq0

\begin{aligned} \left(a+\dfrac1b\right)\left(b+\dfrac1c\right)\left(c+\dfrac1a\right)&=a\cdot b\cdot c+a\cdot b\cdot\dfrac1a+a\cdot\dfrac1c\cdot c+a\cdot\dfrac1c\cdot\dfrac1a+\dfrac1b\cdot b\cdot c+\dfrac1b\cdot b\cdot\dfrac1a+\dfrac1b\cdot\dfrac1c\cdot c+\dfrac1b\cdot\dfrac1c\cdot\dfrac1a\\[8pt] &=abc+b+a+\dfrac1c+c+\dfrac1a+\dfrac1b+\dfrac1{abc}\\[8pt] &=a+\dfrac1b+b+\dfrac1c+c+\dfrac1a+abc+\dfrac1{abc} \end{aligned}