[tex]Jika\\q^{\sqrt[3]{p} }=\sqrt{q}\\q^p=256\\pq=.......[/tex].... Question from @xcvi

$\large\text{$\begin{aligned}pq = \bf2^{61}\end{aligned}$}$

Pembahasan

Diberikan sistem persamaan:

$\large\text{$\begin{cases}q^{\sqrt[3]{p}}=\sqrt{q}&...(i)\\q^p=256&...(ii)\end{cases}$}$

Kita akan menentukan nilai $pq$ .

Dari $(i)$ diperoleh:

$\large\text{$\begin{aligned}&q^{\sqrt[3]{p}}=\sqrt{q}\\&{\rightsquigarrow\ }q^{\sqrt[3]{p}}=q^\frac{1}{2}\\&{\rightsquigarrow\ }\sqrt[3]{p}=\tfrac{1}{2}\\&\therefore\ \ p={\bf\frac{1}{2^3}} \quad...(iii)\end{aligned}$}$

Dari $(ii)$ diperoleh:

$\large\text{$\begin{aligned}q&=256^{\frac{1}{p}}\\&=\left(2^8\right)^{\frac{1}{p}}\\\therefore\ q&={\bf2^\frac{8}{p}}\quad...(iv)\end{aligned}$}$

Sehingga, dari $(iii)$ dan $(iv)$ , dapat diperoleh:

$\large\text{$\begin{aligned}pq&=\frac{1}{2^3}\cdot2^{\left(8/\frac{1}{8}\right)}\\&=\frac{1}{2^3}\cdot2^{8\times8}\\&=\frac{1}{2^3}\cdot2^{64}\\\therefore\ pq&=\boxed{\ \bf2^{61}\ }\end{aligned}$}$

$\blacksquare$

4 votes Thanks 4

xcvi benar!

henriyulianto waduh kirain benul!

henriyulianto terima kasih lagi

xcvi kuis saya masih banyak loh kak

henriyulianto mau tidur dulu. pagi jam 6 harus drive 3 jam utk ngajar

xcvi ok

xcvi Selamat beristirahat ya kak

henriyulianto sama2

Pembahasan

Recommend Questions

Life Enjoy

Get in touch

Social