Finding a and b

[Albi]

How much is a×b if a^2+b^2=1001 and (a-b)^2=1
I am having trouble finding the value of a and b. Any help would be apreciated.

 

[pka]

How much is a×b if a^2+b^2=1001 and (a-b)^2=1

Use the given:
\(a^2-2ab+b^2=(a-b)^2=1\)
\(1001=a^2+b^2=1+2ab\)
\(2ab=1001-1\)
Now finish it !

 

[Albi]

Use the given:
\(a^2-2ab+b^2=(a-b)^2=1\)
\(1001=a^2+b^2=1+2ab\)
\(2ab=1001-1\)
Now finish it !

Use the given:
\(a^2-2ab+b^2=(a-b)^2=1\)
\(1001=a^2+b^2=1+2ab\)
\(2ab=1001-1\)
Now finish it !

Can you explain it a bit more if you don't mind

 

[pka]

Can you explain it a bit more if you don't mind

Do you see that \(a^2-2ab+b^2=(a-b)^2=1~?\)

 

[Albi]

Do you see that \(a^2-2ab+b^2=(a-b)^2=1~?\)

Yeah but how did you get that 1+2ab

 

[pka]

Yeah but how did you get that 1+2ab

Add \(2ab\) to both sides of the equality.

 

[Albi]

Add \(2ab\) to both sides of the equality.

Thanks for taking the time to help

 

[Steven G]

If you have 1 on the rhs of an equation and then suddenly out of nowhere it becomes 1 + 2ab, then surely 2ab was added to the 1--that is 2ab was added to the rhs. So please add 2ab to the lhs. Then things should become clear why this was done. In you case it was to get a^2 + b^2 alone on one side.