Question

5.
The LCM of two numbers is (x + y) and their HCF is P(x - y). If one of the numbers is P, the another
number is
(A) Pxy
(C)x - y2
xy
(D) X+y)
(D) (x-y)
​

Answer 1

Answer:

Second number = x² - y²

Step-by-step explanation:

Let m, n are two numbers.

LCM(m,n) = x+y,

HCF(m,n) = P(x-y),

m = P , n = ?

We know that,

m × n = LCM(m,n) × HCF(m,n)

$n = \frac{LCM \times HCF}{m}$

$= \frac{(x+y)\times P(x-y)}{P}\\=(x+y)(x-y)\\=x^{2}-y^{2}$

Therefore,

Second number = x² - y²

•••♪

Answer 2

The required "option c) $x^{2} -y^{2}$" is correct.

Step-by-step explanation:

Given,

The LCM of two numbers = (x + y), the HCF of two numbers = P(x - y) and

One of the numbers = P

To find, the value of another  number = ?

We know that,

LCM × HCF = The product of two numbers

⇒ (x + y) × P(x - y) = P × Another  number

⇒ $x^{2} -y^{2}$=Another  number

The value of another  number $=x^{2} -y^{2}$

Hence, the required "option c) $x^{2} -y^{2}$" is correct.