Question

Divide 15 into two parts such that the sum of its reciprocal is 3/10

Answer 1

Answer:

Step-by-step explanation:

Let first part be 'x' and second part be '15-x'.

There reciprocals are (1/x) and 1/(15-x) respectively.

According to question-

(1/x) + 1/(15-x) = 3/10

(15-x+x)/[x(15-x)]=3/10

15/(15x-x^2)=3/10

45x-3x^2=150

taking 150 to LHS and Dividing each side by -3

x^2-15x+50=0

This can be written as-

x^2-5x-10x+50=0

x(x-5)-10(x-5)=0

(x-5)(x-10)=0

x=5 and 10

Therefore required numbers are 5 and 10