Question

if and b are positive integers satisfying ab + 2a + 7b - 30 = 0 find GCD of a to thepower 10 - b raised to power 10 , b raised to power 12 - a cube​

Answer 1

Answer:

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Step-by-step explanation:

so its an good problem now seeyou have ab+2a+7b=30 now you have ab+2a+7b+14=44 now you have (b+2)(a+7)=44 now factorize and see case work for integers only one permissible value of b+2 is 4 and that of a+7 is 11 now b=2 a=4 now we have to find gcd(4^10-2^10,2^12-4^3) now use property of gcd that gcd (a,b)=gcd(a,a-b) so use this some times to get that gcd as gcd(2^6(2^6-1),2^6*2^4(2^10-1) now we have to look up for 2^6-1 and 2^10-1 gcd now use again  gcd (a,b)=gcd(a,a-b) and then you will get that you have to look up for gcd of 2^6-1 , 2^6(2^4-1) now so its easy you have to look up for gcd of 63, 2^6(15) which is 3 so our final answer is 2^6*3= 16*3=48 our final answer . a delightful problem liked it to do :)