Question

g(x)g(y)=g(x)+g(y)+g(xy)-2. if g(2)=5 then g(3)=?

Answer 1

can any one

Answer 2

Try finding g(1) first.

Given g(2)=5

g(2)g(1)=g(2)+g(1)+g(2*1)-2 =>
5g(1)=5+g(1)+5-2 =>
g(1)=4

Now
g(1)g(3)=g(1)+g(3)+g(3*1)-2 =>
4g(3)=4+g(3)+g(3)-2 =>
g(3)=1

Answer 3

@mathmate beat me to it :-)

Answer 4

Try finding g(1) first.

Given g(2)=5

g(2)g(1)=g(2)+g(1)+g(2*1)-2 =>
5g(1)=5+g(1)+5-2 =>
g(1)=2 (mistake in previous post)

Now
g(1)g(3)=g(1)+g(3)+g(3*1)-2 =>
2g(3)=2+g(3)+g(3)-2 =>
0=0


Sorry, it doesn't work.

Answer 5

asnaseer, it didn't work out. Hope you have another idea! :)

Answer 6

this is what I was about to post previously:
if you let x=y=2 you will get:\[g(2)*g(2)=g(2)+g(2)+g(4)-2\]\[25=10+g(4)-2\]\[g(4)=17\]maybe you can use similar techniques to solve for g(3)?

Answer 7

we can also find g(0) as follows:
g(0)*g(2)=g(0)+g(2)+g(0)-2
5g(0)=2g(0)+5-2=2g(0)+3
g(0)=1

Answer 8

this leads to:
g(0) = 1
g(1) = 2
g(2) = 5
g(3) = x
g(4) = 17
which could be interpreted as a sequence:
1, 2, 5, x, 17

difference between each term looks like the odd numbers so:
1+1 = 2
2+3 = 5
5+5 = 10
10+7 = 17

so I would say g(3)=10

Answer 9

From g(2)*g(4), we find g(8)=65.

Also, from g(4)=17, we get:
17+(9+11+13+15)=65!

However, it's not a proof.