Los de vierkantsvergelijking op zonder de discriminant te gebruiken
- \(-x^2+36=0\)
- \(x^2-3=3x^2-5\)
- \(7x^2+448=0\)
- \(-7x^2-700=0\)
- \(2x^2-8=0\)
- \(6x^2+600=0\)
- \(3(9x^2-2)=-(-23x^2+6)\)
- \(-2x^2-21=-3x^2+4\)
- \(12x^2+1572=5x^2-3\)
- \(10x^2-2=6x^2+2\)
- \(5x^2-595=8x^2-7\)
- \(5(-7x^2-6)=-(30x^2-470)\)
Los de vierkantsvergelijking op zonder de discriminant te gebruiken
Verbetersleutel
- \(-x^2+36=0 \\
\Leftrightarrow -x^2 = -36 \\
\Leftrightarrow x^2 = \frac{-36}{-1}=36 \\
\Leftrightarrow x = 6 \vee x = -6 \\
V = \Big\{-6, 6 \Big\} \\ -----------------\)
- \(x^2-3=3x^2-5 \\ \Leftrightarrow x^2-3x^2=-5+3 \\
\Leftrightarrow -2x^2 = -2 \\
\Leftrightarrow x^2 = \frac{-2}{-2}=1 \\
\Leftrightarrow x = 1 \vee x = -1 \\
V = \Big\{-1, 1 \Big\} \\ -----------------\)
- \(7x^2+448=0 \\
\Leftrightarrow 7x^2 = -448 \\
\Leftrightarrow x^2 = \frac{-448}{7} < 0 \\
V = \varnothing \\ -----------------\)
- \(-7x^2-700=0 \\
\Leftrightarrow -7x^2 = 700 \\
\Leftrightarrow x^2 = \frac{700}{-7} < 0 \\
V = \varnothing \\ -----------------\)
- \(2x^2-8=0 \\
\Leftrightarrow 2x^2 = 8 \\
\Leftrightarrow x^2 = \frac{8}{2}=4 \\
\Leftrightarrow x = 2 \vee x = -2 \\
V = \Big\{-2, 2 \Big\} \\ -----------------\)
- \(6x^2+600=0 \\
\Leftrightarrow 6x^2 = -600 \\
\Leftrightarrow x^2 = \frac{-600}{6} < 0 \\
V = \varnothing \\ -----------------\)
- \(3(9x^2-2)=-(-23x^2+6) \\ \Leftrightarrow 27x^2-6=23x^2-6 \\
\Leftrightarrow 27x^2-23x^2=-6+6 \\
\Leftrightarrow 4x^2 = 0 \\
\Leftrightarrow x^2 = \frac{0}{4}\\
\Leftrightarrow x = 0 \\
V = \Big\{ 0 \Big\} \\ -----------------\)
- \(-2x^2-21=-3x^2+4 \\ \Leftrightarrow -2x^2+3x^2=4+21 \\
\Leftrightarrow x^2 = 25 \\
\Leftrightarrow x^2 = \frac{25}{1}=25 \\
\Leftrightarrow x = 5 \vee x = -5 \\
V = \Big\{-5, 5 \Big\} \\ -----------------\)
- \(12x^2+1572=5x^2-3 \\ \Leftrightarrow 12x^2-5x^2=-3-1572 \\
\Leftrightarrow 7x^2 = -1575 \\
\Leftrightarrow x^2 = \frac{-1575}{7} < 0 \\
V = \varnothing \\ -----------------\)
- \(10x^2-2=6x^2+2 \\ \Leftrightarrow 10x^2-6x^2=2+2 \\
\Leftrightarrow 4x^2 = 4 \\
\Leftrightarrow x^2 = \frac{4}{4}=1 \\
\Leftrightarrow x = 1 \vee x = -1 \\
V = \Big\{-1, 1 \Big\} \\ -----------------\)
- \(5x^2-595=8x^2-7 \\ \Leftrightarrow 5x^2-8x^2=-7+595 \\
\Leftrightarrow -3x^2 = 588 \\
\Leftrightarrow x^2 = \frac{588}{-3} < 0 \\
V = \varnothing \\ -----------------\)
- \(5(-7x^2-6)=-(30x^2-470) \\ \Leftrightarrow -35x^2-30=-30x^2+470 \\
\Leftrightarrow -35x^2+30x^2=470+30 \\
\Leftrightarrow -5x^2 = 500 \\
\Leftrightarrow x^2 = \frac{500}{-5} < 0 \\
V = \varnothing \\ -----------------\)