Question

Solve by using quadratic formula:

$7. \: 3 {}^{x2 - 5x + 6} = 1$
Ans: 2 , 3

Standard:- 10

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Answer 1

3^( x² - 5x + 6 ) = 1



Multiply by 3 on both sides,


=> 3 × 3^( x² - 5x + 6 ) = 3 × 1

=> 3^( x² - 5x + 6 + 1 ) = 3¹



If bases are equal, powers are same,


=> x² - 5x + 7 = 1

=> x² - 5x + 6 = 0



a = 1
b = -5
c = 6


Discriminant => b² - 4ac
=> (-5)² - 4(1)(6)
=> 25 - 24
=> 1




Applying quadratic equation,

$x = \frac{ - ( - 5) + \sqrt{1} }{2(1)} \: \: \: \: \: \: or \: \: \: \: \: x = \frac{ - ( - 5) - \sqrt{1} }{2} \\ \\ \\ => x = \frac{ 5 + 1}{2} \: \: \: or \: \: \: x = \frac{5 - 1}{2} \\ \\ \\ = > x = 3 \: \: \: \: or \: \: \: x = 2$



Hence, x = 2 or 3