Question

1. 3 = x² - 8x + 8

Explanation:

Step1: Rearrange the equation

Subtract 3 from both sides to set the equation to zero:
\(x^2 - 8x + 8 - 3 = 0\)
Simplify to get:
\(x^2 - 8x + 5 = 0\)

Step2: Use the quadratic formula

The quadratic formula is \(x=\frac{-b\pm\sqrt{b^{2}-4ac}}{2a}\) for an equation \(ax^{2}+bx + c = 0\). Here, \(a = 1\), \(b=-8\), \(c = 5\).
First, calculate the discriminant \(\Delta=b^{2}-4ac=(-8)^{2}-4\times1\times5=64 - 20 = 44\).
Then, find the roots:
\(x=\frac{-(-8)\pm\sqrt{44}}{2\times1}=\frac{8\pm2\sqrt{11}}{2}=4\pm\sqrt{11}\)

Answer:

\(x = 4+\sqrt{11}\) or \(x = 4-\sqrt{11}\)