Question

18. If HCF and LCM of two numbers are respectively (n − 1) and (n² - 1) (n²-4), then the product of the two numbers will be: (a) (²1) (n²-4) (c) (n – 4) (n + 1) (n – 1) (b) (n² + 1) (n²-4) (n² - 1) (d) (n2 _ 1) ( +1) (n−4)​

Answer 1

Given,

HCF of two numbers = (n-1)

LCM of two numbers =  (n² - 1) (n²-4)

To find,

Product of the two numbers

Solution,

Using the rule,

Product of the numbers=Product of HCF and LCM

⇒Product of the numbers=[(n-1){(n² - 1) (n²-4)}]

We know the formula,

$a^{2} -b^{2}= (a+b)(a-b)$

On applying the above formula, we get

⇒Product of the numbers=[(n-1){(n - 1)(n+1) (n-2)(n+2)}]

⇒Product of the numbers=(n-1)²(n+1)(n-1)(n+2)

⇒Product of the numbers=(n-1)²(n+1)(n²-4)

Hence, the product of the numbers is (n-1)²(n+1)(n²-4). Hence, Option c (from the picture) is the correct answer.

Answer 2

Answer:

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