Multiplication the same as addition
Multiplication never gives the same result as addition. Or does it?
If a , b , and c are non-negative integers, b and c are relatively prime, and a + c b = a × c b , then what is b − c ?
The answer is 1.
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3 solutions
What does relatively prime mean?
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Relatively prime means that the integers have no common factors other than 1. Saying that the numerator and denominator of a fraction are 'relatively prime' is another way of saying that the fraction is in reduced terms.
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Oh, that means relatively prime is equivalent to co prime.
x+y=xy is possible only if x and y are equal to 2 ................i know it's pure logic
A couple examples:
3 + 2 3 = 3 × 2 3 = 2 9
7 + 6 7 = 7 × 6 7 = 6 4 9
a + b/c= a*b/c means that a+b/c= b/c+b/c+....+b/c ( a times). just bring one b/c from the right side to the left side and you have : a=(a-1)b/c, now divide both side for ( a-1) and you obtain b=a,c=a-1 so a-(a-1) is equal to 1...my first solution on brilliant..hope you like it
Let y = c b . Then a + y = a y . Solving this equation for y yields y = a − 1 a . Thus, b = a , c = a − 1 , and b − c = 1 .