The HCF and LCM of two numbers M and N are respectly 6 and 210. If M+n = 72.Then 1/m +1/n Is equal to ?
Answers
Answered by
40
As we know
HCF × LCM = product of numbers
6 * 210 = M * N
1260 = M * N
Also, M + N = 72
M = 72 -N
M * N = 1260
( 72 - N) N = 1260
72 N - N² =1260
Or. N² - 72N + 1260 = 0
N² - 42N - 30N + 1260 = 0
N ( N - 42) - 30 ( N - 42) = 0
( N - 42) ( N - 30) = 0
Either N = 42 OR N = 30
AND M = 30 OR M = 42
1 / M + 1/ N =. 1/ 42 + 1/ 30 =
=. ( 30 + 42) / 1260
= 72 / 1260
= 2 / 35
ALTERNATE METHOD ::
1/ M + 1/ n = (m+ n) / mn
= 72 / 1260
= 2/ 35
Hope it helps you
Please mark my answer as brainlist
HCF × LCM = product of numbers
6 * 210 = M * N
1260 = M * N
Also, M + N = 72
M = 72 -N
M * N = 1260
( 72 - N) N = 1260
72 N - N² =1260
Or. N² - 72N + 1260 = 0
N² - 42N - 30N + 1260 = 0
N ( N - 42) - 30 ( N - 42) = 0
( N - 42) ( N - 30) = 0
Either N = 42 OR N = 30
AND M = 30 OR M = 42
1 / M + 1/ N =. 1/ 42 + 1/ 30 =
=. ( 30 + 42) / 1260
= 72 / 1260
= 2 / 35
ALTERNATE METHOD ::
1/ M + 1/ n = (m+ n) / mn
= 72 / 1260
= 2/ 35
Hope it helps you
Please mark my answer as brainlist
Answered by
0
Answer:
2/35
Step-by-step explanation:
Product of the HCF and LCM of two numbers is the same as the product of the numbers themselves. I.e. if m & n are two numbers, mn = LCM x HCF
mn = 6x210 = 1260
m + n = 72 (given)
Now, 1/m + 1/n = (m+n)/mn = 72/1260 = 2/35
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