Question

If 5(a^2-b^2)=100, and a+b=4, what is the value of a-b?

Answer 1

note that:\[a^2-b^2=(a+b)(a-b)\]and that you know that a+b = 4.

Answer 2

I still don't understand, sorry, but can you explain a little bit more? @joemath314159

Answer 3

Sure. So we have:\[5(a^2-b^2)=100\]but as I posted above:\[a^2-b^2=(a+b)(a-b)\]this is a difference of two squares. Now we put that into our equation:\[5(a^2-b^2)=100\Longrightarrow 5(a+b)(a-b)=100\]but you know that a+b=4, so:\[5(a+b)(a-b)=100\Longrightarrow 5\cdot 4 (a-b)=100\]\[\Longrightarrow 20(a-b)=100\]can you solve for a-b from here?

Answer 4

5 (a²-b²)=100
-> a²-b² = 20
=> (a -b) ( a + b ) = 20
Known ( a + b ) = 4
=> (a-b) = ...

Answer 5

Is it 5?

Answer 6

yes :)

Answer 7

Wow, you're much faster than I'm typing for hour :D