Question

( x - 3 )² = ( x - 3 )³

10 - { [ ( x : 4 + 15 ) : 10 + 3 . 2⁴ ] :10 } = 5

Answer 1

\(\left(x-3\right)^2=\left(x-3\right)^3\Leftrightarrow\left(x-3\right)^3-\left(x-3\right)^2=0\)

\(\Leftrightarrow\left(x-3\right)^2\left[x-3-1\right]=0\Leftrightarrow\left(x-3\right)^2\left(x-4\right)=0\Leftrightarrow x=3;x=4\)

\(10-\left\{\left[\left(x:4+15\right):10+3.2^4\right]:10\right\}=5\)

\(\Leftrightarrow\left[\left(\dfrac{x}{4}+15\right):10+3.16\right]:10=5\)

\(\Leftrightarrow\left(\dfrac{x}{4}+15\right):10+48=50\Leftrightarrow\left(\dfrac{x}{4}+15\right):10=2\Leftrightarrow\dfrac{x}{4}+15=20\)

\(\Leftrightarrow x=20\)