Question

If a2+b2=45 and ab=18, then the value
of 1/a+1/b is
a b
is​

Answer 1

Answer:

1/a + 1/b = 1/2

Step-by-step explanation:

a^2 + b^2 = 45 and ab = 18

a^2 + b^2 + 2ab = 45 + 2*18

                           = 45 + 36

                           = 81

But a^2 + 2ab + b^2 = (a+b)^2

Thus, (a+b)^2 = 81

(a+b) = 9

Now,

1/a + 1/b = (a+b)/ab

Substituting values, we get:

1/a + 1/b = 9/18

              = 1/2

Please note that -1/2 could also be a solution, because

if (a+b)^2 = 81, then (a+b) = 9 or -9