Question

If f(x) =x^2-3x+4, then find the values of x satisfying the equation f(x) =f(2x+1).​

Answer 1

Answer:

-1 and 2/3

Step-by-step explanation:

Hello, please consider the following.

$f(x)=f(2x+1)\\\\\begin{aligned}<=> x^2-3x+4&=(2x+1)^2-3(2x+1)+4\\\\&=4x^2+4x+1-6x-3+4\\\\&=4x^2-2x+2\end{aligned}\\\\<=> x^2-3x+4=4x^2-2x+2\\\\<=> 3x^2+x-2=0$

$\Delta=b^2-4ac=1+4*2*3=25=5^2\\\\x_1=\dfrac{-1-5}{6}=-1\\\\x_2=\dfrac{-1+5}{6}=\dfrac{4}{6}=\dfrac{2}{3}$

Thank you