a+b=5......(1)

a*b=2......(2)

From (2) : a= 2/b or =2/a

Substitute in (1)

2/b +b =5

==> 2+b^2 =5b

==> b^2 = 5b-2....(3)

2/a+ a =5

==> 2+a^2 =5a

==> a^2 = 5a -2 ....(4)

Add (3) and (4)

==> a^2 +b^2 = 5(a+b)-4

= 5(5)-4= 21

Now we need to calculate a/b + b/a

a/b + b/a = (a^2 +b^2)/ab = 21/ 2= 10.5

Given a+b=5 and a*b = 2. To find a/b+b/a

Solution:

a/b+b/a = (a^2+b^2)/ab = {(a+b)^2-2ab}/ab. Putting give values, we get

= {5^2-2*2}/2 = 21/2 =10.5

First, in order to add the quotients a/b and b/a, they have to have the same denominator, which is a*b. For this reason, we'll multiply the first quotient by a and the second quotient by b.

(a/b)+(b/a)=a*(a/b)+b*(b/a)=(a^2 +b^2)/a*b

We'll add and subtract the same amount at numerator, namely2*a*b, and we'll group the terms in a convenient way, so that we'll get:

[(a^2+2*a*b +b^2)-2*a*b]/a*b=(a+b)^2/a*b - 2=21/2

Now, we'll substitute the sum and the product of the numbers a and b, by the values given in the enunciation:

**(a+b)^2/a*b - 2 = 25/2 - 2 = (25-4)/2 = 21/2**