Question

The sum of two numbers is 8 and 15 times the sum of their reciprocals is also 8. Find the numbers.

Answer 1

let the no.s are 'a' and b'

a+b = 8

15(1/a + 1/b) = 8

15(a+b) = 8ab
ab = 15

here now form quadratic who's zeroes are a and b

which is
x²-8x+15 = 0

x = [8±√[64-60]]÷2
= [8±√4]/2
= 4±1

then a and b are
3 and 5

no.s are
3 and 5

hope it helps you
@di

Answer 2

Answer:

3 and 5

Step-by-step explanation:

#let the two no. be x and y

#x+y=8------(i)

#x=8-y---------(ii)

#15[1/x+1/y]=8

#1/x+1/y=8/15

#x+y/(x)(y)=8/15

#1/(x)(y)={8/15}(x+y)

#1/(x)(y)={8/15}(8)--------    [equation-(i)]  

#1/(x)(y)=1/15

#xy=15

#(8-y)(y)=15-------------[equation-(ii)]

#y^2-8y+15=0

#y^2-5y-3y+15=0

#y(y-5)-3(y-5)=0

#(y-3)(y-5)=0

#so,y= 3 and 5        {y-3=0  and   y-5=0}

                                {y=3      and   y=5}

#putting the value in equation second:x=8-y

#if y=3                     #if y=5

#x=8-3                     #x=8-5

#x=5                        #x=3

#so the tow no. are 3 and 5 [x=3 or 5 ;y=5 or 3]