Question

two natura numbers differ by 3 an sum of whose reciprocals is 7/10 find the numbers

Answer 1

let the two numbers be x and y
according to the question
x-y=3 equation 1
1/x+1/y=7/10 equation 2

from equation 2
y+x/yx=7/10
10(y+x)=7yx equation 3

from equation 1
x=3+y

putting value of x in equation 3
10(y+3+y)=7y(3+y)
10(2y+3)=21y+7y^2
20y+30=21y+7y^2
7y^2+21y -20y-30=0
7y^2+y-30=0
7y^2-14y+15y-30=0
7y(y-2)+15(y-2)=0
(7y+15) (y-2)=0

if y=-15/7
putting value of y in equation 1
x-(-15/7)=3
x+15/7=3
7x+15=21
x=6/7

if value of y is 2
putting the value of y in equation 1

x-2=3
x=5



hope it helps you