Question

The sum and product of two numbers are 12 and 35 respectively. W
bers are 12 and 35 respectively. What will be the sum of their
reciprocals?
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Answer 1

Answer:

12 / 35

Step-by-step explanation:

Given---> Sum and product of two numbers are 12 and 35 respectively.

To find ---> Sum of reciprocals of numbers.

Solution---> Let numbers be a and b .

Now ATQ

Sum of numbers = 12

=> a + b = 12

Product of numbers = 35

Now we have to find sum of reciprocals of the numbers

Now first we understand the term reciprocal of a number

If we have a number then reciprocal of it is equal to the one divided by that number

Reciprocal of a number = 1 ÷ number

= 1 / number

Now

Reciprocal of ' a ' = 1 ÷ a

= 1 / a

Reciprocal of ' b ' = 1 ÷ b

= 1 / b

Now ,sum of reciprocal of numbers

= 1 / a + 1 / b

LCM of a and b is ab

= b + a / ab

We know that

b + a = a + b (commutativity of addition)

So putting , b + a = a + b we get

= a + b / ab

Now putting a + b = 12 and ab = 35 we get

Sum of reciprocals of number = 12 / 35

Answer 2

Answer:

Step-by-step explanation:

let 2 numbers are x and y

sum of the number is

$x+y=12$

There product is

$xy = 35$

the sum of reciprocal is

$(\frac{1}{x} )+(\frac{1}{y} )$

$\frac{x+y}{xy}$

$\frac{12}{35}$

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