Question

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Answer 1

a)
$(4x)^2+(3x)^2=20^2 \\ 16x^2+9x^2=400 \\ 25x^2=400 \\ x^2=\frac{400}{25} \\ x^2=16 \\ \boxed{x=4}$

b)
$x^{2} +6^2=(3\sqrt5)^2 \\ x^2+36=45 \\ x^2=45-36 \\ x^2=9 \\ \boxed{x=3}$

c)
$(x+1)^2=x^2+(\sqrt7)^2 \\ x^2+2x+1=x^2+7 \\ 2x+1=7 \\ 2x=7-1 \\ 2x=6 \\ \boxed{x=3}$

d)
$x^2+x^2=(3\sqrt2)^2 \\ 2x^2=18 \\ x^2=\frac{18}{2} \\ x^2=9 \\ \boxed{x=3}$