Explicație pas cu pas:
a)
[tex] \frac{ \sqrt{3} - x}{4} + \frac{1}{ \sqrt{3} } = \frac{x}{6} \\ \frac{ \sqrt{3} - x }{4} + \frac{ \sqrt{3} }{3} = \frac{x}{6} \\ 3( \sqrt{3} - x) + 4 \sqrt{3} = 2x \\ 3 \sqrt{3} - 3x + 4 \sqrt{3} = 2x \\ 7 \sqrt{3} - 3x = 2x \\ - 3x - 2x = - 7 \sqrt{3} \\ - 5x = - 7 \sqrt{3} \\ x = \frac{7 \sqrt{3} }{5} [/tex]
c)
[tex] \frac{ \sqrt{2x} - \sqrt{8} }{ \sqrt{2} } + \frac{ \sqrt{3x} - \sqrt{12} }{ \sqrt{3} } = 5 \\ \frac{ \sqrt{2x} - 2 \sqrt{2} }{ \sqrt{2} } + \frac{ \sqrt{3x} - 2 \sqrt{3} }{ \sqrt{3} } = 5 \\ \frac{ \sqrt{2} ( \sqrt{x} - 2)}{ \sqrt{2} } + \frac{ \sqrt{3} ( \sqrt{x} - 2) }{ \sqrt{3} } = 5 \\ \sqrt{x} - 2 + \sqrt{x} - 2 = 5 \\ 2 \sqrt{x} - 4 = 5 \\ 2 \sqrt{x } = 5 + 4 \\ 2 \sqrt{x} = 9 \\ \sqrt{x} = \frac{9}{2} \\ x = \frac{9 {}^{2} }{2 {}^{2} } \\ x = \frac{81}{4} \\ x = 20 \times \frac{1}{4} [/tex]
d)
[tex] \frac{ \sqrt{5x} + \sqrt{2} }{ \sqrt{5} } + \frac{ \sqrt{3x} - \sqrt{5} }{ \sqrt{3} } = \sqrt{2} + \frac{ \sqrt{10} }{5} - \frac{ \sqrt{15} }{3} \\ 15 \sqrt{3} ( \sqrt{5x} + \sqrt{2} ) + 15 \sqrt{5} ( \sqrt{3x} - \sqrt{5} ) = 15 \sqrt{30} + 3 \sqrt{150} - 75 \\ 15 \sqrt{15x} + 15 \sqrt{6} + 15 \sqrt{15x} - 75 = 15 \sqrt{30} + 15 \sqrt{6} - 75 \\ 15 \sqrt{15x} + 15 \sqrt{15x} = 15 \sqrt{30} \\ 30 \sqrt{15x} = 15 \sqrt{30} \\ \sqrt{15x} = \frac{ \sqrt{30} }{2} \\ 15x = \frac{30}{4} = \frac{15}{2} \\ x = \frac{1}{2} [/tex]
Sper ca te-am ajutat :)
