# Thread: [SOLVED] Prove (a + b) is not an integer

1. ## [SOLVED] Prove (a + b) is not an integer

Hi, can someone answer this asap. Thanks !

a and b are numbers where a=b+2
the sum of a and b is equal to the product of a and b
Show that a + b are not intergers

Thankyou to anyone who can help. I need
the working out as well as the answer plz.

2. Originally Posted by Hannah95
Hi, can someone answer this asap. Thanks !

a and b are numbers where a=b+2
the sum of a and b is equal to the product of a and b
Show that a + b are not intergers

Thankyou to anyone who can help. I need
the working out as well as the answer plz.
Hi Hannah,

1]$\displaystyle a=b+2$

2]$\displaystyle a+b=ab$

Substitute 1] into 2]

$\displaystyle (b+2)+b=(b+2)b$

$\displaystyle 2b+2=b^2+2b$

$\displaystyle 2=b^2$

$\displaystyle \boxed{b=\sqrt{2}}$

$\displaystyle \boxed{a=\sqrt{2}+2}$

$\displaystyle a+b=\sqrt{2}+2+\sqrt{2}=2+2\sqrt{2}$

Q.E.D. a + b is not an integer.

3. Thankyou !!! Masters. Its really easy when you know what to do.
Thankyou again !!!

Hannah