Question

Solve each of the following equations:


`(4 )/(9) - \frac{x {}^(2) }{25} = 0`
​

Answer 1

`x = 3(1)/(3), \: \: x = - 3(1)/(3)`

Explanation:

`(4 )/(9) - \frac{x {}^(2) }{25} = 0 \\ \\ = { \bigg( (2)/(3) \bigg) }^(2) - { \bigg( (x)/(5) \bigg) }^(2) = 0\\ \\ { \bigg( (2)/(3) -(x)/(5) \bigg) }{ \bigg( (2)/(3) + (x)/(5) \bigg) } = 0 \\ \\ { \bigg( (2)/(3) -(x)/(5) \bigg) } = 0, \: \: { \bigg( (2)/(3) + (x)/(5) \bigg) } = 0 \\ \\ (x)/(5) = (2)/(3), \: \: (x)/(5) = - (2)/(3) \\ \\ x = (10)/(3), \: \: x = - (10)/(3) \\ \\ x = 3(1)/(3), \: \: x = - 3(1)/(3) \\ \\`