5^х+125*5^-х=30 кто сможет решить.

(5^ (-х) = 1 / 5^x) : 5^х + 125 * (1 / 5^x) = 30; 5^х + 125/5^x = 30

((5^х*5^х + 125) / 5^х = 30; (5^ (2 х) + 125) / 5^х = 30; 5^ (2 х) + 125 = 30*5^х

5^ (2 х) - 30*5^х + 125 = 0.

5^ (2 х) = t^2, 5^х = t. t^2 - 30t + 125 = 0.

D = b^2 - 4ac = (-30) ^2 - 4*1*125 = 900 - 500 = 400.

t = (-b + / - √D) / 2a. t1 = ( - (-30) + √400) / 2*1 = (30 + 20) / 2 = 50/2 = 25.

t2 = ( - (-30) - √400) / 2*1 = (30 - 20) / 2 = 10/2 = 5.

1) 5^х = t1; 5^х = 25; 5^х = 5^2;

х1 = 2.

2) 5^х = t2; 5^х = 5; 5^х = 5^1;

х2 = 1.

Ответ: х1 = 2; х2 = 1.