Question

If sum of two numbers is 10.Find the maximum value of the sum of their reciprocals?​

Answer 1

Answer:

sum of two no.=10

sum of their reciprocal=5/12

CALCULATION:

let the no. be x and y

so,x+y=10 ...(i)

and,(1/x)+(1/y)=5/12 ....(ii)

= (x+y)/xy=5/12

now,

=10/xy=5/12

xy=12×2=24....(iii)

Now,(10-y)× y=24

=10y-y²=24

=y²-10y+24=0

=y²-6y-4y+24=0

=y(y-6)-4(y-6)=0

=(y-6)(y-4)=0

=y=6,4