Question

If a ^1÷x=b^1÷3 and ab = 1, prove that x + 3 = 0.​

Answer 1

$\bf \large \bold{Hola!}$

• GiveN :

$\mapsto \sf \: {a}^{ \frac{1}{x} } = {b}^{ \frac{1}{3} }$

$\sf \mapsto \: ab = 1$

___________________________

• ShoW ThaT :

$\mapsto \sf \: x + 3 = 0$

___________________________

• ProoF :

$\mapsto \: \: \sf \: {a}^{ \frac{1}{x} } = {b}^{ \frac{1}{3} } \: \: \: \: [ \: Given \: ]$

$\mapsto \sf \: \: \: {a}^{ \frac{1}{x} } = {a}^{ - \frac{1}{3} } \: \: \: [ \: as \:\: ab=1 \:; \: \implies \:\: b=\frac{1}{a} ]$

$\mapsto \sf \: \: \: \: \frac{1}{x} = - \frac{1}{3}$

$\sf \mapsto \: \: \: \: \frac{3}{x} + 1 = 0$

$\sf \therefore \: \: \: \: \: \: { \underline{ \boxed{ \sf{ 3 + x = 0}}}} \: \: \: [ \: Proved \: ]$

____________________

HAVE A WONDERFUL DAY...