Question

please solve this..........​

Answer 1

$Given \: 5 \cdot 5^{x} + \frac{5}{5^{x}} = 26$

$Let \: a = 5^{x} \: --(1)$

$\implies 5a + \frac{5}{a} = 26$

$\implies \frac{5a^{2} + 5}{a} = 26$

$\implies 5a^{2} + 5 = 26a$

$\implies 5a^{2} - 26a + 5 = 0$

/* Splitting the middle term, we get */

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

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

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

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

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

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

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

$\implies x = 1 \:Or \: x = -1$

Therefore.,

$\green { x = 1 \:Or \: x = -1}$

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Answer 2

Answer:

$(x - 1)(x - 2)(x - 3)(x - 4) = 120 = 2 \times 3 \times 4 \times 5$

so comparing both sides we get

$x - 1 = 5 \: \: so \: \: x = 6$