Question

just refer to the picture and find the value of X​

Answer 1

Answer:

2

Step-by-step explanation:

We have

$x = \frac{2}{3-\frac{2}{3-\frac{2}{3-\frac{2}{\frac{7-3x}{3-x}}}}}= \frac{2}{3-\frac{2}{3-\frac{2}{3-\frac{6-2x}{7-3x}}}}}=\frac{2}{3-\frac{2}{3-\frac{2}{\frac{15-7x}{7-3x}}}}}=\frac{2}{3-\frac{2}{3-\frac{14-6x}{15-7x}}}=\frac{2}{3-\frac{2}{31-15x}}=\frac{62-30x}{91-45x}.$ So, $91x-45x^2=62-30x$ and $45x^2-121x+62=0$. By the quadratic formula, we have $\frac{-(-121) \pm \sqrt{121^2-4(45)(62)}}{45 \cdot 2} = \frac{121 \pm 59}{90}.$ Simple testing from here shows that x = 2.