Question

If a square +b square =45&ab=18,then 1/a+1/b is

Answer 1

Hola there,

According to the question,

=> a² + b² = 45. and ab = 18

Now, as we know,

=> (a + b)² = a² + b² + 2ab

Putting values we get

=> (a + b)² = 45 + 36

=> (a + b)² = 81

=> a + b = 9. ... equation 1

From given, ab = 18

We can write b = 18/a

Put the value in equation 1, we get..

=> a + 18/a = 9

=> a² + 18 = 9a

=> a² - 9a + 18 = 0

=> a² - 3a - 6a + 18 = 0

=> a(a - 3) -6(a - 3) = 0

=> (a - 3)(a - 6) = 0

=> a = 3 or 6

Now b = 18/3 or 18/6

= 6 or 3

So, 1/a + 1/b when a = 3 and b = 3

= 2/3


1/a + 1/b when a = 6 and b = 6

= 2/6 = 1/3


1/a + 1/b when a = 6 and b = 3

= 3/6 = 1/2


1/a + 1/b when a = 3 and b = 6

= 3/6 = 1/2

Hope this helps....:)