5.
[tex]a) \frac{1}{9} {x}^{2} = 16 \\ \frac{ {x}^{2} }{9} = 16 \\ {x}^{2} = 9 \times 16 \\ {x}^{2} = 144 \\ x = \sqrt{144}x = 12[/tex]
[tex] \frac{1}{100} {x}^{2} - \frac{1}{64} = 0 < = > \frac{ {x}^{2} }{100} = \frac{1}{64 } \\ {x}^{2} \times 64 = 100 < = > {x}^{2} = \frac{100}{64} \\ x = \sqrt{ \frac{100}{64} } = > x = \frac{10}{8} = \frac{5}{4} [/tex]
[tex] \frac{1}{25} {x}^{2} = 0.49 < = > \frac{ {x}^{2} }{25} = \frac{49}{100} \\ {x }^{2} \times 100 = 49 \times 25 \\ {x}^{2} \times 100 = 1225 \\ {x}^{2} = \frac{1225}{100} = > {x}^{2} = 12.25 \\ x = \sqrt{12.25} = 3.5 [/tex]
[tex]b)2 {x}^{2} = 3 < = > {x}^{2} = \frac{3}{2} < = > x = \sqrt{ \frac{3}{2} } \\ x = \frac{ \sqrt{3} }{ \sqrt{2} } < = > x = \frac{ \sqrt{6} }{2} [/tex]
[tex]c)9 {x}^{2} - 10 = 0 < = > 9 {x}^{2} = 10 < = > {x}^{2} = \frac{10}{9} < = > x = \sqrt{ \frac{10}{9} } \\ x = \frac{ \sqrt{10} }{3} [/tex]
