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

**Hannah95** · February 11th 2009, 11:48 AM

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.

**masters** · February 11th 2009, 01:00 PM

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] $a=b+2$

2] $a+b=ab$

Substitute 1] into 2]

$(b+2)+b=(b+2)b$

$2b+2=b^2+2b$

$2=b^2$

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

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

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

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

**Hannah95** · February 12th 2009, 04:38 AM

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

Hannah

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