Question

If
$3.2 {}^{2x + 1} - 5.2 {}^{x + 2} + 16 = 0$
and x is an integer , find the value of x.
plzz explanation needed!

Answer 1

here is the solution for ur ans hope u like it plz brainiest...

Answer 2

Hi..☺

Here is your answer...✌


$3. {2}^{2x + 1} - 5. {2}^{x + 2} + 16 = 0 \\ \\ 3. {2}^{2x} . {2}^{1} - 5. {2}^{x} . {2}^{2} + 16 = 0 \\ \\ 6( {2}^{x} ) {}^{2} - 20( {2}^{x} ) + 16 = 0 \\ \\ let \: \: {2}^{x} = m \: \\ therefore \\ \\ 6 {m}^{2} - 20m + 16 = 0 \\ \\ 3 {m}^{2} - 10m + 8 = 0 \\ \\ 3 {m}^{2} - 6m - 4m + 8 = 0 \\ \\ 3m(m - 2) - 4(m - 2) = 0 \\ \\ (3m - 4)(m - 2) = 0 \\ \\ = > m = \frac{4}{3} \: \: or \: \: m = 2 \\ \\ = > {2}^{x} = \frac{4}{3} \: \: or \: \: {2}^{x} = 2 \\ \\ = > {2}^{x} = 2 \: \: \: \: \: ( \: since \: x \: is \: an \: integer \:) \\ \\on \: equating \: the \: exponent \: of \:2 \\ \\ = > x = 1$