Question

if x and y are natural numbers, log 8+log 5=log(x+y)+log(x y) and log 8+log 11=log(x)+log(1+xy). then find the value of (x³-y³).​

Answer 1

Given : x and y are natural numbers

log 8+log 5=log(x+y)+log(x y) and log 8+log 11=log(x)+log(1+xy)

To find :  the value of (x³-y³).​

Solution:

log 8+log 5=log(x+y)+log(x y)

=> log ( 8 * 5) = log (( x + y)(xy))

=>  8 * 5  =  xy(x + y)   Eq1

Similarly

8* 11 =  x ( 1 + xy)   Eq2

Eq2 / Eq1

11/5  = (1 + xy)/y(x + y)

=> 11y(x + y)  = 5  + 5xy

=> y (11x +11y)  = 5 + 5xy

=>  y ( 11x  + 11y  - 5x)  = 5

=> y ( 11y + 6x)  = 5

as x and y are natural numbers

Hence least value of   y ( 11y + 6x)  be  1(11 + 6) = 17

Hence it seems there is mistake in data

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