All Answers 358512 Answers

a = 337   (prime)

b = 1685 = 5.337

gcd(a,b) = 337,   lcm(a,b) = 1685

5.gcd(a,b) =5.337 = 1685 = lcm(a,b).

Ty so much!

That wasn't right

I added 8+(-1/2) and got 7.5 or 15/2 and it was still wrong... did I add the wrong numbers?!

F(x) = (x^3 + 4x)/(x^2 + 4).

The roundness of 1,000,000 is 15.

Just plug in the values.

Like so:

\(\frac{(a−b)}{a} =\frac{ b}{(a−b)}\\ (a-b)^2=ab\\ a^2-2ab+b^2=ab\\ a^2-3ab+b^2=0\\ a^2+(-3b)a+(b^2)=0\\ a=\frac{3b\pm\sqrt{9b^2-4b^2}}{2}\\ a=\frac{3b\pm b\sqrt{5}}{2}\\ \)

\(a=\frac{3b\pm b\sqrt{5}}{2}\\ \frac{a}{b}=\frac{3\pm \sqrt{5}}{2}\\ \text{if you add those two possibilities the sum is } 6/2 = 3 \)

You neeed to check this carefully.

An exhaustive computer search show that the answer is 40:

2 + 3 + 5 + 6 + 7 + 8 + 9 = 40

1*4*10 = 40

ok so we break it down 

12! has 4 "3" factors and 1 "9" factor

so that's 1+4=5

15! has 5 "3's" and 1 "9"

so that's 5+1=6

18! has 6 "3's" and 2 "9's"

so that's 6+2=8

21! has 7 "3's" and 2 "9's"

so that's 7+2=9

24! has 8 "3's" and 2 "9's"

so that's 8+2=10 factors of 3

so its basicaly 3^5 + 3^6 + 3^8 + 3^9 + 3^10 

simplify that to (3^5)(1 + 3 + 3^3 + 3^4 + 3^5)

1 + 3 + 3^3 + 3^4 + 3^5 is not divisible by 3

so it's 3^5

I think

1/a + 1/b = 14/5.

The possible values of m are 7 and 13.

x^2 +7x -44

ax^2+bx+c

we already know a is 1, for it's given

x^2+bx+c

b is just sum of roots which is just 11+(-4)=7

x^2+7x+c

c is just the product of the roots which is 11x(-4)=-44

so it's just x^2 + 7x - 44

These are all perfect squares.

225 = \(15^2\)

4 = \(2^2\)

169 = \(13^2\)

196 = \(14^2\)

400 = \(20^2\)

121 = \(11^2\)

Thanks, Alan!

Thanks!

The exponent of 3 is 14.