Math, asked by sarahbadran5, 1 year ago

an integer x written as a product of its prime factor is ( a to the power of 2 * 7 to the power b + 2) . an integer Y written as a product of its prime factor is ( a to the power of 3 * 7 to the power of 2) the highest common factor of X and Y is 1225. the lowest common multiple of X and Y is 42875. what is the value of X and Y.

Answers

Answered by mannya2
3

sorry boys I don't know if I will put comment that I have to search on this it's a good quite complicated questions of the Year

Answered by nauranazh
58

Answer:

X=8575

Y=6125

Step-by-step explanation:

I know I'm late but i'm putting this up just incase someone has troubles on solving the question too :D

HCF of X and Y is 1225

you take the smallest exponent that the prime number are both present in both numbers, in this case:

a^2 from X, and 7^2 from Y ---> we're solving for A

a^2 x 7^2 = 1225

a^2 x 49 = 1225

a^2 = 25

a = sqrt of 25

a = 5

LCM of X and Y is 42875

you take the biggest exponent! - we don't care if it doesn't reoccur in other number, in this case:

5^3 x 7^b+2 = 42875

125 x 7^b+2 = 42875

7^b+2 = 343 --> make 343 having the same root number of 7

7^b+2 = 7^3 --> remove the 7s, just to have the exponents

b+2 = 3

b = 1

SO now,

X: 5^2 x 7^3 = 8575

Y: 5^3 x 7^2 = 6125

i hope it helps :) and i'm sorry if i don't explain it too clearly

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