3.
$$f ( x ) = x ^ { 2 } - 10 x + 23$$
- Express \(\mathrm { f } ( x )\) in the form \(( x + a ) ^ { 2 } + b\), where \(a\) and \(b\) are constants to be found.
- Hence, or otherwise, find the exact solutions to the equation
$$x ^ { 2 } - 10 x + 23 = 0$$
- Use your answer to part (b) to find the larger solution to the equation
$$y - 10 y ^ { 0.5 } + 23 = 0$$
Write your solution in the form \(p + q \sqrt { r }\), where \(p , q\) and \(r\) are integers.