Robert Bosch Algebra Quiz 3

Explanation:

\frac{\sqrt{3+x} + \sqrt{3-x}}{\sqrt{3+x} - \sqrt{3-x} }  = \frac{2}{1}  

By componendo and dividendo,

Þ   \frac{2*\sqrt{3+x}}{2*\sqrt{3-x}}  = \frac{2+1}{2-1}=3  

Squaring on both sides, we get

  \frac{3+x}{3-x}= 9  

Þ 3 + x = 27 – 9x

Þ 9x + x = 27 – 3 = 24

Þ   x = \frac{24}{10} = \frac{12}{5}  

Explanation:

\sqrt{2^ x} = 256   

Þ   2^{\frac{x}{2}} = 2^{8}  

Þ   \frac{x}{2} = 8  

 Þ x = 16

Explanation:

Given that

a * b = 2a + 3b – ab

  \therefore 3*5 + 5 *3  

= (2 *3 + 3 * 5 – 3 * 5) + (5 * 2+ 3* 3 – 5 * 3)

= (6 + 15 – 15) + (10 + 9 – 15)

= 6 + 4 = 10

Explanation:

   \sqrt(1 + \frac{x}{9}) = \frac{13}{3}   

Squaring both sides,    \sqrt(1 + \frac{x}{9}) = \frac{169}{9}  

  \frac{x}{9} =\frac{169}{9} -1 = \frac{160}{9}  

  x = \frac{160}{9} *9 = 160   

Explanation:

 x + y = 2z

Þ x = 2z – y 

Þ x – z = 2z – y – z = z – y

   \frac{x}{x}- z+ \frac{z}{y}-z   

   \frac{x}{x}- z- \frac{z}{z}-y     

    \frac{x}{x}- z - \frac{z}{x}-z   

 =  x- \frac{z}{x}-z = 1  

 

Explanation:

 a * b =  a ^{b}  

   \therefore 5 * 3 = 5^{3}   

 = 5 * 5* 5 = 125

Explanation:

  \sqrt{0.03\times 0.3a} = 0.3 \times 0.3 \times \sqrt{b}   

On squaring,

  0.03\times 0.3\times a = 0.09 \times 0.09\times b   

=>    \frac{a}{b} =  0.09 \times \frac{0.09}{0.03} \times0.3  

= 0.9

Explanation:

x* y = (x + 3)^{2} * (y – 1)

\therefore  5* 4 = (5 + 3)^{2} *(4 – 1) 

= 64* 3 = 192

Explanation:

9\sqrt{x} = \sqrt{3*2*2} =  \sqrt{3*7*7}

9\sqrt{x} = 2\sqrt{3} +  7\sqrt{3} =  9\sqrt{3}

x=3

Explanation:

X * Y = X^{2} + Y^{2} – XY

\therefore 11 * 13 = 11^{2} + 13^{2} – 11* 13

= 121 + 169 – 143

 = 147