Question

If 51+x + 51-x=26 then the values of x are

Answer 1

Answer:

it is wrong pls correct it

I think the question will be 51+x-(51-x)=26

2x=26

x=13

Answer 2

we have,

${5}^{1 + x} + 5 {}^{1 - x} = 26$

$\rightarrow \: 5.5 {}^{x} + 5.5 {}^{ - x} = 26$

$putting \: \: {5}^{x} = y$

$5y + \frac{5}{y} = 26$

$5 {y}^{2} + 5 = 26y$

$\rightarrow \: {5y}^{2} - 26 + 5 = 0$

$\rightarrow \: 5 {y}^{2} - 25y - y + 5 = 0$

$\rightarrow \: 5y(y - 5) - 1(y - 5) = 0$

$\rightarrow \: (y - 5)(5y - 1) = 0$

$y - 5 = 0 \: \: and \: \: 5y - 1 = 0$

so,

y = 5 or y = 1/5

$5 {}^{x} = {5}^{1} \: or \: {5}^{x} = {5}^{ - 1}$

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

Hence, the roots of the given equation are 1, -1