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3 years ago

6/a - 4/b = 1 and 9/a - 8/b = 1

Mathematics

1 answer:

Alja [10]3 years ago

5 0

Answer:

a = 3 ; b = 4

Step-by-step explanation:

Eqn.1 = $\frac{6}{a} - \frac{4}{b} = 1$

Eqn.2 = $\frac{9}{a} - \frac{8}{b} = 1$

Both the eqns have RHS (Right Hand Side) equal. So,

$\frac{6}{a} - \frac{4}{b} = \frac{9}{a} - \frac{8}{b}$

$= > \frac{6b - 4a}{ab} = \frac{9b - 8a}{ab}$

Cancelling ab from both the denominators of both the sides,

$= > 6b - 4a = 9b - 8a$

$= > 8a - 4a = 9b - 6b$

$= > 4a = 3b$

$= > a = \frac{3b}{4}$

Putting the value of a in Eqn.1,

$\frac{6}{ \frac{3b}{4} } - \frac{4}{b} = 1$

$= > \frac{24}{3b} - \frac{4}{b} = 1$

$= > \frac{8}{b} - \frac{4}{b} = 1$

$= > \frac{8 - 4}{b} = 1$

$= > b = 4$

Putting the value of b in the value of a

$a = \frac{3 \times 4}{4} = 3$

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Step-by-step explanation:

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A King in ancient times agreed to reward the inventor of chess with one grain of wheat on the first of the 64 squares of a chess

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Answer:

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