164/MR00. problem / Math - Solved Math Problems

MR-164. problem

Solve the following equation:

$(5 x - 3) (5 x + 3) - (3 x + 5) (3 x - 5) = 0$

$(5 x - 3) (5 x + 3) - (3 x + 5) (3 x - 5) = 0$

$(25 x^{2} - 9) - (9 x^{2} - 25) = 0$

25 x^{2} - 9 - 9 x^{2} + 25 = 0

16 x^{2} + 16 = 0

16 x (x^{2} + 1) = 0

x^{2} + 1 = 0

x^{2} = - 1

x_{1, 2} = \pm \sqrt{- 1}

x_{1, 2} = \pm i

$x_{1} = + i; x_{2} = - i$

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