SOLUTION: If a,b, and c are positive integers, find the sum a + b + c if:
{{{a^3b^3c = 454425283}}}, {{{a^3bc^3 = 248258803}}} and {{{ab^3c^3 = 777094123}}}
Algebra.Com
Question 1199209: If a,b, and c are positive integers, find the sum a + b + c if:
, and
Answer by greenestamps(13203) (Show Source): You can put this solution on YOUR website!
For this one, you definitely want to use an online calculator to find the prime factorization... unless you have nothing better to do with your time.
454425283 = (13^3)(17^1)(23^3)
You could use the online calculator again to find the prime factorizations of the other two numbers. But you don't have to, because you already know that
(a^3)(b^3)(c) = (13^3)(17)(23^3),
so you know that c is 17 and a and b are, in some order, 13 and 23. And since you are only asked to find the sum a+b+c, you have all the information you need to do that.
ANSWER: a+b+c = 13+17+23 = 53
RELATED QUESTIONS
If a,b,and c are positive integers, find the sum a+b+c if {{{ a^3bc = 7776 }}} and {{{... (answered by Shin123)
If a, b, and c are positive integers, find the sum a+b+c if {{{ a^3bc = 7776 }}}, {{{... (answered by ikleyn)
If a,b and c are positive integers, find the sum a+b+c if:
{{{a^3b^2c = 3528, ab^3c^2 =... (answered by greenestamps)
If {{{ a^2b^3c^4=648000 }}}, where a, b and c are distinct positive integers greater than (answered by greenestamps,math_tutor2020)
A, B, C and D are positive integers such that A^2 + 3B^2 + 3C^2 + 5D^5 = 1002. What is... (answered by ikleyn)
Let a, b,c be positive integers with a>=b>=c such that
a^2 - b^2 - c^2 +ab=2011
and... (answered by richard1234)
If a, b, and c are positive integers, find the sum a+b+c if (a^3)(b)=1375, (b^3)(c)=3993... (answered by ikleyn)
If a+c=-8 and c-b=-4, find the value of {{{3a^2-6b^20+3c^2}}}.
CC11F... (answered by greenestamps,ikleyn)
If a, b, and c are positive integers, find the sum a+b+c if {{{ (a^3)*b=1375 }}} , {{{... (answered by ikleyn,greenestamps)