the difference of two natural numbers is 5 and the difference of their reciprocal is 1 by10 .Find the numbers?
Answers
Let the first number be x. If x>second number, then second number is x-5 If x<second number then second number is 5+x ATQ When numbers are x and x-5 1/x-5 - 1/x=1/10(As the larger number has smaller reciprocal) x-x+5/(x-5)(x)=1/10 50=x^2-5x x^2-5x-50=0 x^2-10x+5x-50=0 x(x-10)+5(x-10)=0 (x-10)(x+5)=0 x=10,-5 x can't be -5 as it is a natural number So we will ignore -5. So x=10. So first number is 10 and second number is 10-5=5 When numbers are x and x+5 1/x - 1/x+5=1/10(As the larger number has smaller reciprocal) x+5-x/(x+5)(x)=1/10 50=x^2+5x x^2+5x-50=0 x^2+10x-5x-50=0 x(x+10)-5(x+10)=0 (x+10)(x-5)=0 x=-10,5 x can't be -10 as it is a natural number So we will ignore -10. So x=5. So first number is 5 and second number is 5+5=10 So the numbers are either 5,10 or 10,5