Question

a^2+b^2 =45 and ab=18 find 1/a +1/b​

Answer 1

Answer:

1/2

Step-by-step explanation:

a²+b² = 45

First we have to find a-b

So,

(a-b)² = a² + b² - 2ab

→ (a-b)² = 45 - 2(18)

→ (a-b)² = 45 - 36

→ (a-b)² = 9

→ a-b = √9 = 3 ------(i)

Again now, we have to find a+b

(a+b)² = a² + b² + 2ab

→ (a+b)² = 45 + 2(18)

→ (a+b)² = 45 + 36

→ (a+b)² = 81

→ a+b = √81 = 9 ------(ii)

Now adding (i) and (ii)

a+b = 9

a-b = 3

------------

2a = 12

a = 6

Now putting the value of 'a' in equation (i)

a-b = 3

6-b = 3

-b = 3-6

-b = -3

b = 3

Now, a = 6 and b = 3

Now we have to find 1/a + 1/b

1/a + 1/b

→ 1/6 + 1/3

→ 1+2/6

→ 3/6

→1/2