Question

If lcm of two numbers is 105 and hcf of two numbers is 1 ,the sum of two numbers is 22,find the difference of two numbers

Answer 1

Answer:

8

Step-by-step explanation:

If lcm of two numbers is 105 and hcf of two numbers is 1 ,the sum of two numbers is 22,find the difference of two numbers

Let Say Numbers are

A & B

A * B = LCM * HCF

=> AB = 105 * 1

=> AB = 105

A + B = 22

=> B = 22-A

=> A(22-A) = 105

=> -A² + 22A = 105

=> A² -22A + 105 = 0

=> A² - 7A - 15A + 105 = 0

=> A(A-7) -15(A-7) = 0

=> (A - 15)(A-7) = 0

=> A = 15 or 7

so B = 7 or 15

Difference of Two numbers = 15-7 = 8

or Difference can be found without findind number

AB = 105

A + B = 22

Squaring Both side

A² + B² + 2AB = 484

(A - B)² + 4AB = 484

(A - B)² + 4*105 = 484

=> (A-B)² = 64

=> A- B = ± 8

Difference of numbers = 8