Q1.If HCF and LCM of two positive numbers (a,b) is 2 and 24 respectively and the sum of the two numbers is 14, find the positive numbers a and b.
Answers
Answered by
6
Explanation:
Answer:
The numbers are 8 and 6.
Step-by-step explanation:
The two numbers = a and b
HCF and LCM of a and b = 2 and 24
Sum of the numbers = 14
According to the Question,
⟶ a + b = 14
⟶ a = 14 - b ----- (Equation I)
We know that,
★ HCF × LCM = Product of numbers
⟶ 2 × 24 = a × b
⟶ 48 = (14 - b) × b
⟶ 48 = -b² + 14b
⟶ b² - 14b + 48 = 0
⟶ b² - 6b - 8b + 48 = 0
⟶ b(b - 6) - 8(b - 6) = 0
⟶ (b - 6)(b - 8) = 0
⟶ b = 6 or b = 8
Taking b as 6, substitute the value of b in equation I.
⟶ a = 14 - 6
⟶ a = 8
The numbers are :
a = 8
a = 8b = 6
Therefore, the numbers are 8 and 6.
Answered by
0
Answer:
a = 6
b = 8
Or vice versa as you need it
Explanation:
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