Question

como resolvo (3x-1)²-(X-1)²=0

Answer 1

$\boxed{\boxed{a^{2}-b^{2}=(a+b)\cdot(a-b)}}$
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$(3x-1)^{2}-(x-1)^{2}=0\\([3x-1]+[x-1])\cdot([3x-1]-[x-1])=0\\(3x-1+x-1)\cdot(3x-1-x+1)=0\\(4x-2)\cdot(2x)=0$

O produto será nulo se:

$4x - 2 = 0\\4x=2\\x=2/4\\x=1/2$

Ou:

$2x=0\\x=0/2\\x=0\\\\\\\boxed{\boxed{S=\{0,~\dfrac{1}{2}\}}}$