Math, asked by ziya02, 1 year ago

the different of two number is 4 if the difference of their reciprocal is 4/21,then find two numbers

Answers

Answered by Panzer786
24
Heya !!!



Let two numbers be X and Y.



According to question,



Difference of two numbers =>4



X - Y = 4 --------(1)





Reciprocal of X is 1/X and Reciprocal of Y is 1/Y.





1/X - 1/Y = 4/21



Y - X / XY = 4/21




21(Y - X ) = 4XY



21Y - 21X = 4XY -------(2)


From equation (1) we get,







X - Y = 4



X = 4 + Y ------(3)




Putting the value of X in equation (2)





21Y - 21X = 4XY




21Y - 21 ( 4 + Y) = 4(4+Y) × Y





21Y - 84 - 21Y = (16 + 4Y)Y




-84 = 16Y + 4Y²





4Y² + 16Y + 84 = 0




4Y² + 28Y - 12Y + 84 = 0




4Y ( Y + 7 ) - 12 ( Y + 7) = 0



( Y + 7) ( 4Y - 12) = 0




(Y+7) = 0 OR (4Y-12) = 0



Y = -7 OR Y = 12/4 = 3





Putting Y = 3 in equation (3)




X = 4 +Y




X = 4+3 = 7




Hence,




Two numbers are 7 and 3.



★ ★ ★ HOPE IT WILL HELP YOU ★ ★ ★

ziya02: tq
Answered by Aerrika
5
let larger number be x and smaller be y then x-y=4and,1/x-1/y=4/21x-y/xy=4/214/xy=4/21xy= 21x+y = √[x-y]²+4xy       = √4²+4×21       = √16+84       = √100 =10thus we have x-y=4         equation 1                      x+y=10      equation 2on solving 1 and 2 we get                       x=7 and y=-3   or we can also take √100=-10then we have x-y = 4 and x+y = -10   on solving we get x = -3 and y = -7hence required numbers are 7 and 3 and -3 and -7
                  


Similar questions