a)
[tex](4x)^2+(3x)^2=20^2 \\
16x^2+9x^2=400 \\
25x^2=400 \\
x^2=\frac{400}{25} \\
x^2=16 \\
\boxed{x=4}[/tex]
b)
[tex] x^{2} +6^2=(3\sqrt5)^2 \\
x^2+36=45 \\
x^2=45-36 \\
x^2=9 \\
\boxed{x=3}[/tex]
c)
[tex](x+1)^2=x^2+(\sqrt7)^2 \\
x^2+2x+1=x^2+7 \\
2x+1=7 \\
2x=7-1 \\
2x=6 \\
\boxed{x=3}[/tex]
d)
[tex]x^2+x^2=(3\sqrt2)^2 \\
2x^2=18 \\
x^2=\frac{18}{2} \\
x^2=9 \\
\boxed{x=3}[/tex]
