Question

The sum of two number no 25 and sum of their reciprocal is 1/4 find no.

Answer 1

Answer:

x=15 and y=10.

Step-by-step explanation:

x+y=25

1/x+1/y=1/4

(x+y)/xy=1/4

x+y=xy/4

xy=(x+y)×4=25×4=100

Again, x²+y²=(x+y)²-2xy

=25²-200

=625-200=425

Again, x²-y²=(x+y)²-4xy

=25²-400

=625-400=225

So, x²+y²-(x²-y²)=425-225

or, x²+y²-x²+y²=200

or, 2y²=200

or, y²=100

or, y=10

So, x=25-10=15.