Question

If the sum of two numbers is 20 and their hcf and lcm are 1 and 91 respectively,then the square of one of the number is

Answer 1

let the two numbers are a and b then, we take lcm 91. 91 =7*13*1 ,the no.s are 13and 7 now we checked it, 13+7=20 hence this is right then the square of one no. is 49(7*7)

Answer 2

Answer:

If the number is 7 then square is 49 and

If the number is 13 then the square is 169

Step-by-step explanation:

Let the two numbers be a and b

According to question, the sum of two numbers is 20

⇒ a + b = 20

Value of b from above equation

b = 20 - a

Also, we are given LCM = 91 and HCF = 1

We know ,

LCM * HCF = Product of two numbers

LCM * HCF = a * b

Substituting the value of HCF , LCM and b from above,

91 * 1 = a * ( 20 - a )

91 = 20 a - a²

a² - 20b + 91 = 0

a² - 13a - 7a + 91 = 0

a ( a - 13 ) - 7 ( a - 13 ) = 0

( a - 7 ) ( a - 13 ) = 0

Taking ( a - 7 ) = 0

a = 7

Taking ( a - 13 ) = 0

a= 13

Values of a can be 7 or 13

Now,

b = 20 - a

For a = 7 , b = 20  - 7 = 13

For a = 13 , b = 20 - 13 = 7

Hence the numbers are  7 and 13

Square of the numbers are 49 and 169