Example

3(r+2s)=2t-4
a⋅(b-2)=3b
3(r+2s)=2t-4
a⋅(b-2)=3b

Question

$${ x }^{ 2 } + { y }^{ 2 } = { z }^{ 2 }$$

Answer

x=sqrt((z+y)*(z-y)),-sqrt((z+y)*(z-y))

Solution


Subtract \({y}^{2}\) from both sides.
\[{x}^{2}={z}^{2}-{y}^{2}\]
Use Difference of Squares: \({a}^{2}-{b}^{2}=(a+b)(a-b)\).
\[{x}^{2}=(z+y)(z-y)\]
Take the square root of both sides.
\[x=\pm \sqrt{(z+y)(z-y)}\]
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