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- #1

#### Albert

##### Well-known member

- Jan 25, 2013

- 1,225

ab=1

bc=2

cd=3

de=4

ea=5

find a,b,c,d,e

bc=2

cd=3

de=4

ea=5

find a,b,c,d,e

- Thread starter Albert
- Start date

- Thread starter
- #1

- Jan 25, 2013

- 1,225

ab=1

bc=2

cd=3

de=4

ea=5

find a,b,c,d,e

bc=2

cd=3

de=4

ea=5

find a,b,c,d,e

- Admin
- #2

- Feb 14, 2012

- 3,690

From $ab=1$ and $bc=2$, we have: $2ab=bc$ $2ab-bc=0$ $b(2a-c)=0$ Since $b \ne 0$, $2a-c=0$ must be true or $c=2a$. | From $cd=3$ and $c=2a$, we have: $(2a)d=3$ $2ad=3$ | From $de=4$ and $ea=5$ and $2ad=3$, we have: $ade^2=4(5)$ $2ad(e^2)=2(20)$ $3(e^2)=40$ $\therefore e=\pm 2\sqrt{\dfrac{10}{3}}$ | $\begin{align*}\therefore a&=\dfrac{5}{e}\\&=\pm \dfrac{5}{2}\sqrt{\dfrac{3}{10}}\end{align*}$ $\begin{align*}\therefore d&=\dfrac{3}{2a}\\&=\pm \dfrac{3}{5}\sqrt{\dfrac{10}{3}}\end{align*}$ $\begin{align*}\therefore c&=\dfrac{3}{d}\\&=\pm 5 \sqrt{\dfrac{3}{10}}\end{align*}$ $\begin{align*}\therefore b&=\dfrac{1}{a}\\&=\pm \dfrac{2}{5}\sqrt{\dfrac{10}{3}}\end{align*}$ |

- Mar 31, 2013

- 1,309

Or abcde = +/-120$^{(1/2)}$

Devide by product of ab and cd to get e = = +/-120$^{(1/2)}$/ 3= = +/-(40/3)$^{(1/2})$ = +/-2(10/3)$^{(1/2)}$

Similarly you can find the rest

- Mar 31, 2013

- 1,309

From $ab=1$ and $bc=2$, we have:

$2ab=bc$

$2ab-bc=0$

$b(2a-c)=0$

Since $b \ne 0$, $2a-c=0$ must be true or $c=2a$.From $cd=3$ and $c=2a$, we have:

$(2a)d=3$

$2ad=3$From $de=4$ and $ea=5$ and $2ad=3$, we have:

$ade^2=4(5)$

$2ad(e^2)=2(20)$

$3(e^2)=40$

$\therefore e=\pm 2\sqrt{\dfrac{10}{3}}$$\begin{align*}\therefore a&=\dfrac{5}{e}\\&=\pm \dfrac{5}{2}\sqrt{\dfrac{3}{10}}\end{align*}$

$\begin{align*}\therefore d&=\dfrac{3}{2a}\\&=\pm \dfrac{3}{5}\sqrt{\dfrac{10}{3}}\end{align*}$

$\begin{align*}\therefore c&=\dfrac{3}{d}\\&=\pm 5 \sqrt{\dfrac{3}{10}}\end{align*}$

$\begin{align*}\therefore b&=\dfrac{1}{a}\\&=\pm \dfrac{2}{5}\sqrt{\dfrac{10}{3}}\end{align*}$

I thought that it may be noted that all are positive or all are -ve. I know you know it but for benefit of others

- Admin
- #5

I thought that it may be noted that all are positive or all are -ve. I know you know it but for benefit of others

Yes, you can see that all of the values **anemone** found inherit their sign from $e$.

- Admin
- #6

- Feb 14, 2012

- 3,690

The \sqrt{} command creates a square root surrounding an expression.As I do not know how to put square root I have put power 1/2

Take for example, \sqrt{x} gives $\sqrt{x}$.

Well done,

Or abcde = +/-120$^{(1/2)}$

Devide by product of ab and cd to get e = = +/-120$^{(1/2)}$/ 3= = +/-(40/3)$^{(1/2})$ = +/-2(10/3)$^{(1/2)}$

Similarly you can find the rest

- Thread starter
- #7

- Jan 25, 2013

- 1,225

good solution

Or abcde = +/-120$^{(1/2)}$

Devide by product of ab and cd to get e = = +/-120$^{(1/2)}$/ 3= = +/-(40/3)$^{(1/2})$ = +/-2(10/3)$^{(1/2)}$

Similarly you can find the rest

the use of square root example :type :" \sqrt[m]{b^n} " between two "dollar signals"

you will get: $\sqrt[m]{b^n}$