Решите уравнение 5²ˣ⁺¹ = 5ˣ+4

Question

Алгебра

Raivimlos

5 год назад

Решите уравнение 5²ˣ⁺¹ = 5ˣ+4

ОТВЕТЫ

Leanapal

Jun 30, 2019

$5^{2x+1}=5^{x+4}\\amp;#10;2x+1=x+4\\amp;#10;2x-x=4-1\\amp;#10;x=3$

$5^{2x+1}=5^x+4\\amp;#10;5^{2x}*5-5^x-4=0\\amp;#10;5^x=m, \ m\ \textgreater \ 0\\amp;#10;5m^2-m-4=0\\amp;#10;a+b+c=0 \ (5-1-4=0) \ =\ \textgreater \ \ m=1, \ m=-4/5\\amp;#10;5^x=1\\amp;#10;5^x=5^0\\amp;#10;x=0$

$5^{2x+1}=5^{x} +4amp;#10;amp;#10; 5^{x} =t; t\ \textgreater \ 0amp;#10;amp;#10;5t^{2}-t-4=0; D=1+4*4*5=81;amp;#10;amp;#10;t_{1}= \frac{1+ \sqrt{81} }{10} = 1;amp;#10;amp;#10;t_{2}= \frac{1- \sqrt{81} }{10} = -0.8;$
Из них подходит только корень t=1;
$5^{x}=1;amp;#10;amp;#10;x = 0$

17