QUESTION I Solve for \( x \) : \( \begin{array}{l}1.1 \quad x(2 x-7)=-3 \\ 1.2 \quad \sqrt{x+5}+x=3 \quad \text { [correct to } 2 \text { decimal places) } \\ 1.3 \quad-x^{2}+16>0 \\ 1.4 \quad \text { Solve for } x \text { and } y \text { simultaneously, } \\ \quad x-3 y=1 \text { and }(2 x+y-1)(x-y+1)=0 \\ 1.5 \quad \text { Prove that: } \\ \sqrt{\sqrt[1]{a b}} \cdot \sqrt{b \sqrt[y]{a}}=a^{\frac{2+s}{s s}} b^{\frac{b+s}{n s}}\end{array} \)

First additional information: Understanding how to solve quadratic equations like \( x(2x - 7) = -3 \) can boost your algebra skills! Rearranging to standard form \( 2x^2 - 7x + 3 = 0 \) allows you to apply the quadratic formula, \( x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \). It's like solving a puzzle where each piece leads closer to the answer! Second additional information: When dealing with inequalities like \( -x^2 + 16 > 0 \), remember that rewriting it as \( x^2 < 16 \) gives \( -4 < x < 4 \). It's essential to analyze the solutions' impact on any real-world scenarios, such as predicting range limits, just like racing cars needing to stay within certain speed bounds for a safe track experience!