2 years ago

What is the solution to the equation below -2+ square root 3x-2=6

Mathematics

1 answer:

never [62]2 years ago

7 0

Answer:

Step-by-step explanation:

Given

- 2 + $\sqrt{3x-2}$ = 6 ( isolate the radical by adding 2 to both sides )

$\sqrt{3x-2}$ = 8 ( square both sides )

3x - 2 = 8² = 64 ( add 2 to both sides )

3x = 66 ( divide both sides by 3 )

x = 22 → A

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A system of equations is shown

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$\bf \begin{cases}
\boxed{y}=3x-2\\
y=x^2
\end{cases}~\hspace{6em}\stackrel{\textit{doing a quick substitution}}{\boxed{3x-2}=x^2}\implies 0=x^2-3x+2
\\\\\\
0=(x-1)(x-2)\implies
\begin{cases}
0=x-1\implies &1=x\\[0.8em]
0=x-2\implies &2=x
\end{cases}
\\\\[-0.35em]
~\dotfill$

$\bf \stackrel{\textit{using x = 1 in the first equation}}{y=3(1)-2\implies y=1}~\hfill \blacktriangleright (\stackrel{x}{1},\stackrel{y}{1}) \blacktriangleleft
\\\\\\
\stackrel{\textit{using x = 2 in the first equation}}{y=3(2)-2\implies y=4}~\hfill \blacktriangleright (\stackrel{x}{2},\stackrel{y}{4})\blacktriangleleft$