Question

№99(2) Розв'яжіть рівняння:
2) (5х)⁷*(5х)⁴*25/(25х³)⁴*125х=1

Answer 1

$\displaystyle\bf\\\frac{(5x)^7\cdot(5x)^4\cdot 25}{(25x^{3)^4} \cdot 125x} =1\\\\\\(5x)^{7} \cdot (5x)^4\cdot 25=(5x)^4\cdot(5x^{2} )^{4} \cdot 5x\cdot 25\\\\\\(5x)^{7} =(5x)^4\cdot x^{4} \cdot 5x\\\\\\(5x)^{2} = x^{4} \\\\x^{4} -25x^{2} =0\\\\x^{2} \cdot(x^{2}-25)=0 \\\\x^{2} \cdot(x-5)\cdot(x+5)=0\\\\x_{1} =0- \ ne \ podxodit\\\\x-5=0 \ \ \Rightarrow \ \ x_{2} =5\\\\x+5=0 \ \ \Rightarrow \ \ x_{3} =-5\\\\Otvet \ : \ \ 5 \ ; \ -5$