1-3-a-2-2-a-

Question Number 140863 by mathdanisur last updated on 13/May/21

1 + \sqrt{3^{a}} = 2 \sqrt{2^{a}}

Commented by mr W last updated on 13/May/21

a = 0 o r 2

Commented by mathdanisur last updated on 13/May/21

t h a n k s d e a r S i r s o l u t i o n s p l e a s e

Commented by mr W last updated on 13/May/21

t h e r e i s n o f o r m u l a t o c a l c u l a t e t h e

s o l u t i o n . i n t h i s s p e c i a l c a s e y o u c a n

“ {s e e}^{″} t h e s o l u t i o n i s a = 0 o r 2, b e c a u s e

t h e y a r e o b v i o u s .

i f t h e q u e s t i o n i s 1 + \sqrt{3^{a}} = 3 \sqrt{2^{a}} t h e n

t h e s o l u t i o n i s n o t o b v i o u s . i t h i n k

t h e r e i s n o w a y t o g e t t h e e x a c t

s o l u t i o n .

t h r o u g h s u c h q u e s t i o n s o n e c a n

l e a r n n o t h i n g a n d o n e c a n t e a c h

n o t h i n g .

Commented by mathdanisur last updated on 13/May/21

t h a n k y o u d e a r S i r ★

Answered by ajfour last updated on 14/May/21

p^{2} = 3^{a} q^{2} = 2^{a}

\Rightarrow 2 \ln p = a \ln 3

2 \ln q = a \ln 2

p = \frac{3 q}{2}

1 + p = 2 q

1 + 3 q = 2 q

\Rightarrow q = - 1

\Rightarrow 2^{a} = 1 \Rightarrow a = 0

p = - 3

3^{a} = 9 \Rightarrow a = 2

Commented by prakash jain last updated on 14/May/21

How did you get p = \frac{3 q}{2} ?

Commented by bramlexs22 last updated on 14/May/21

\Leftrightarrow a = a

\Leftrightarrow \frac{2 l n p}{\ln 3} = \frac{2 l n q}{\ln 2}

\Leftrightarrow \ln p = \frac{\ln 3 . \ln q}{\ln 2}

\Rightarrow \ln p = \frac{\ln q^{\ln 3}}{\ln 2}

\Rightarrow \ln p = \ln q^{\ln 3^{\frac{1}{\ln 2}}}

\Rightarrow p = q^{\ln 3^{\frac{1}{\ln 2}}}

Commented by prakash jain last updated on 14/May/21

It {isn}^{'} t same as p = \frac{3 q}{2}