Exercise 17

The numeric value of the expression:   \( \cfrac{ 3 x^2 y \sqrt{ 2x + y } }{ \sqrt{ 4x^2 + 4xy + y^2 } } \)   when   \( x = 1 \)   and   \( y = -1 \)   is:

The numeric value of the expression:

\[ \frac{ 3 x^2 y \sqrt{ 2x + y } }{ \sqrt{ 4x^2 + 4xy + y^2 } } \]

when   \( x = 1 \)   and   \( y = -1 \)   is:

  1. \( 1 \)

  2. \( -1 \)

  3. \( 3 \)

  4. \( -3 \)

  5. \( 0 \)

Try to solve it before checking the answer.

  1. \( -3 \)

\[ \begin{aligned} &\frac{ 3 (1)^2 (-1) \sqrt{ 2(1) + (-1) } }{ \sqrt{ 4(1)^2 + 4(1) (-1) + (-1)^2 } } \\[1em] &\hspace{8em}= \frac{ -3 \sqrt{2 – 1} }{ \sqrt{4 – 4 + 1} } \\[1em] &\hspace{8em}= \frac{-3}{1} \\[1em] &\hspace{8em}= \boldsymbol{-3} \end{aligned} \]
\[ \begin{aligned} \frac{ 3 (1)^2 (-1) \sqrt{ 2(1) + (-1) } }{ \sqrt{ 4(1)^2 + 4(1) (-1) + (-1)^2 } } &= \frac{ -3 \sqrt{2 – 1} }{ \sqrt{4 – 4 + 1} } \\[1em] &= \frac{-3}{1} \\[1em] &= \boldsymbol{-3} \end{aligned} \]

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