Question

2. The sum of two numbers is 18. If the sum of the
reciprocals is
find the numbers.
4.
1​

Answer 1

Correct Question:-

The sum of two numbers is 18. If the sum of their reciprocals is 1/4 , find the numbers.

Answer:-

Given:

Sum of two numbers = 18

Let the numbers be "a" and "b".

Hence,

→ a + b = 18 -- equation (1)

And,

Sum of their reciprocals = 1/4

→ 1/a + 1/b = 1/4

Taking LCM in LHS we get,

→ (b + a) / ab = 1/4

Putting the value of "(a + b)" from equation (1) we get,

→ (18)/ab = 1/4

On cross multiplication we get,

→ 18 * 4 = (1) * (ab)

→ 72 = ab - equation (2)

We know that,

(a - b)² = (a + b)² - 4ab

Hence,

(a - b)² = (18)² - 4 * 72

→ (a - b)² = 324 - 288

→ (a - b)² = 36

→ (a - b)² = (6)²

→ (a - b) = 6 -- equation (3)

Adding equations (1) & (3) we get,

→ a + b + a - b = 18 + 6

→ 2a = 24

→ a = 24/2

→ a = 12

Substitute the value of a in equation (1)

→ a + b = 18

→ 12 + b = 18

→ b = 18 - 12

→ b = 6

Hence, the two numbers are 12 & 6.

Answer 2

Answer:

Step-by-step explanation:

Given

sum of two numbers is 18

sum of their reciprocals is 1/4

Let us consider a and b are two numbers

so a+b = 18

1/a + 1/b = 1/4

Please find the attached file

I hope this will help you..

Good day!