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Solve the equation
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$y = \sqrt{ 3 } x + x$
$y = 10$
$x$Intercept
$\left ( 0 , 0 \right )$
$y$Intercept
$\left ( 0 , 0 \right )$
$x = 5 \sqrt{ 3 } - 5$
$ $ Solve a solution to $ x$
$\sqrt{ \color{#FF6800}{ 3 } } \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ x } = 10$
$ $ Organize the expression $ $
$\left ( \sqrt{ \color{#FF6800}{ 3 } } \color{#FF6800}{ + } \color{#FF6800}{ 1 } \right ) \color{#FF6800}{ x } = 10$
$\left ( \sqrt{ \color{#FF6800}{ 3 } } \color{#FF6800}{ + } \color{#FF6800}{ 1 } \right ) \color{#FF6800}{ x } = \color{#FF6800}{ 10 }$
$ $ Divide both sides by the same number $ $
$\color{#FF6800}{ x } = \color{#FF6800}{ \dfrac { \color{#FF6800}{ 10 } } { \sqrt{ \color{#FF6800}{ 3 } } \color{#FF6800}{ + } \color{#FF6800}{ 1 } } }$
$x = \dfrac { 10 } { \sqrt{ 3 } + 1 }$
$ $ Find the conjugate irrational number of denominator $ $
$x = \color{#FF6800}{ \dfrac { \color{#FF6800}{ 10 } } { \sqrt{ \color{#FF6800}{ 3 } } \color{#FF6800}{ + } \color{#FF6800}{ 1 } } } \color{#FF6800}{ \times } \color{#FF6800}{ \dfrac { \sqrt{ \color{#FF6800}{ 3 } } \color{#FF6800}{ - } \color{#FF6800}{ 1 } } { \sqrt{ \color{#FF6800}{ 3 } } \color{#FF6800}{ - } \color{#FF6800}{ 1 } } }$
$x = \dfrac { 10 } { \sqrt{ 3 } + 1 } \times \dfrac { \sqrt{ 3 } - 1 } { \sqrt{ 3 } - 1 }$
$ $ The denominator is multiplied by denominator, and the numerator is multiplied by numerator $ $
$x = \color{#FF6800}{ \dfrac { \color{#FF6800}{ 10 } \left ( \sqrt{ \color{#FF6800}{ 3 } } \color{#FF6800}{ - } \color{#FF6800}{ 1 } \right ) } { \left ( \sqrt{ \color{#FF6800}{ 3 } } \color{#FF6800}{ + } \color{#FF6800}{ 1 } \right ) \left ( \sqrt{ \color{#FF6800}{ 3 } } \color{#FF6800}{ - } \color{#FF6800}{ 1 } \right ) } }$
$x = \dfrac { \color{#FF6800}{ 10 } \left ( \sqrt{ \color{#FF6800}{ 3 } } \color{#FF6800}{ - } \color{#FF6800}{ 1 } \right ) } { \left ( \sqrt{ 3 } + 1 \right ) \left ( \sqrt{ 3 } - 1 \right ) }$
$ $ Multiply each term in parentheses by $ 10$
$x = \dfrac { \color{#FF6800}{ 10 } \sqrt{ \color{#FF6800}{ 3 } } \color{#FF6800}{ - } \color{#FF6800}{ 10 } } { \left ( \sqrt{ 3 } + 1 \right ) \left ( \sqrt{ 3 } - 1 \right ) }$
$x = \dfrac { 10 \sqrt{ 3 } - 10 } { \left ( \sqrt{ \color{#FF6800}{ 3 } } \color{#FF6800}{ + } \color{#FF6800}{ 1 } \right ) \left ( \sqrt{ \color{#FF6800}{ 3 } } \color{#FF6800}{ - } \color{#FF6800}{ 1 } \right ) }$
$ $ Expand the expression using $ \left(a - b\right)\left(a + b\right) = a^{2} - b^{2}$
$x = \dfrac { 10 \sqrt{ 3 } - 10 } { \left ( \sqrt{ \color{#FF6800}{ 3 } } \right ) ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ - } \color{#FF6800}{ 1 } ^ { \color{#FF6800}{ 2 } } }$
$\color{#FF6800}{ x } = \color{#FF6800}{ \dfrac { \color{#FF6800}{ 10 } \sqrt{ \color{#FF6800}{ 3 } } \color{#FF6800}{ - } \color{#FF6800}{ 10 } } { \left ( \sqrt{ \color{#FF6800}{ 3 } } \right ) ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ - } \color{#FF6800}{ 1 } ^ { \color{#FF6800}{ 2 } } } }$
$ $ Organize the expression $ $
$\color{#FF6800}{ x } = \color{#FF6800}{ \dfrac { \color{#FF6800}{ 10 } \sqrt{ \color{#FF6800}{ 3 } } \color{#FF6800}{ - } \color{#FF6800}{ 10 } } { \color{#FF6800}{ 2 } } }$
$x = \color{#FF6800}{ \dfrac { \color{#FF6800}{ 10 } \sqrt{ \color{#FF6800}{ 3 } } \color{#FF6800}{ - } \color{#FF6800}{ 10 } } { \color{#FF6800}{ 2 } } }$
$ $ Reduce the fraction $ $
$x = \color{#FF6800}{ 5 } \sqrt{ \color{#FF6800}{ 3 } } \color{#FF6800}{ - } \color{#FF6800}{ 5 }$
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