First slide

Theory of equations

Question

The number of negative roots of
$9^{x + 2} - 6 (3^{x + 1}) + 1 = 0$ is

Moderate

A

0
B

1
C

2
D

4

Solution

$9^{x + 2} - 6 (3^{x + 1}) + 1 = 0$
Put $3^{x + 1} = t$ so that $t^{2} - 6 t + 1 = 0$
$\Rightarrow t = \frac{6 \pm \sqrt{32}}{2} = 3 \pm 2 \sqrt{2}$
$\Rightarrow x + 1 = \log_{3} (3 + 2 \sqrt{2}) > 1$
or $x + 1 = \log_{3} (3 - 2 \sqrt{2}) < 0$

Get Instant Solutions

When in doubt download our app. Now available Google Play Store- Doubts App

Recieve an sms with download link

Doubts App

OR

SCAN ME

Doubts App

Doubts App