Question

Solve 5 x+1 + 5 2-x=126

Answer 1

hope it will be helpful to you

Answer 2

Answer:

$x = 2 \: or \: x = -1$

Step-by-step explanation:

$5^{x+1}+5^{2-x}=126$

$\implies 5^{x}\times 5^{1}+\frac{5^{2}}{5^{x}}=126$

$Let \: 5^{x}=a$

$\implies 5a+\frac{25}{a}=126$

$\implies \frac{5a^{2}+25}{a}=126$

$\implies 5a^{2}+25=126a$

$\implies 5a^{2}-126a+25=0$

/* Splitting the middle term,we get */

$\implies 5a^{2}-125a-1a+25=0$

$\implies 5a(a-25)-1(a-25)=0$

$\implies (a-25)(5a-1)=0$

$\implies a-25 = 0\:Or\: 5a-1=0$

$\implies a=25 \:Or\: 5a=1$

$\implies a=25 \:Or\: a=\frac{1}{5}$

$\implies a=5^{2}\:Or\: a=5^{-1}$

$Now,\\5^{x}=5^{2}\:Or\:5^{x}=5^{-1}$

$x = 2 \: or \: x = -1$

$Since, \: If \:a^{m}=a^{n} \: then \: m=n$

Therefore,

$x = 2 \: or \: x = -1$

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