Los de vierkantsvergelijking op zonder de discriminant te gebruiken
- \(-2x^2+50=0\)
- \(8x^2-1352=0\)
- \(3x^2+0=0\)
- \(-14x^2+152=-8x^2+2\)
- \(-7x^2+252=-2x^2+7\)
- \(7x^2+7=0\)
- \(-3x^2-372=-6x^2-9\)
- \(-8x^2-200=0\)
- \(9x^2-6=7x^2-6\)
- \(-10x^2+187=-6x^2-9\)
- \(2x^2-338=0\)
- \(11x^2-12=9x^2-4\)
Los de vierkantsvergelijking op zonder de discriminant te gebruiken
Verbetersleutel
- \(-2x^2+50=0 \\
\Leftrightarrow -2x^2 = -50 \\
\Leftrightarrow x^2 = \frac{-50}{-2}=25 \\
\Leftrightarrow x = 5 \vee x = -5 \\
V = \Big\{-5, 5 \Big\} \\ -----------------\)
- \(8x^2-1352=0 \\
\Leftrightarrow 8x^2 = 1352 \\
\Leftrightarrow x^2 = \frac{1352}{8}=169 \\
\Leftrightarrow x = 13 \vee x = -13 \\
V = \Big\{-13, 13 \Big\} \\ -----------------\)
- \(3x^2+0=0 \\
\Leftrightarrow 3x^2 = 0 \\
\Leftrightarrow x^2 = \frac{0}{3}\\
\Leftrightarrow x = 0 \\
V = \Big\{ 0 \Big\} \\ -----------------\)
- \(-14x^2+152=-8x^2+2 \\ \Leftrightarrow -14x^2+8x^2=2-152 \\
\Leftrightarrow -6x^2 = -150 \\
\Leftrightarrow x^2 = \frac{-150}{-6}=25 \\
\Leftrightarrow x = 5 \vee x = -5 \\
V = \Big\{-5, 5 \Big\} \\ -----------------\)
- \(-7x^2+252=-2x^2+7 \\ \Leftrightarrow -7x^2+2x^2=7-252 \\
\Leftrightarrow -5x^2 = -245 \\
\Leftrightarrow x^2 = \frac{-245}{-5}=49 \\
\Leftrightarrow x = 7 \vee x = -7 \\
V = \Big\{-7, 7 \Big\} \\ -----------------\)
- \(7x^2+7=0 \\
\Leftrightarrow 7x^2 = -7 \\
\Leftrightarrow x^2 = \frac{-7}{7} < 0 \\
V = \varnothing \\ -----------------\)
- \(-3x^2-372=-6x^2-9 \\ \Leftrightarrow -3x^2+6x^2=-9+372 \\
\Leftrightarrow 3x^2 = 363 \\
\Leftrightarrow x^2 = \frac{363}{3}=121 \\
\Leftrightarrow x = 11 \vee x = -11 \\
V = \Big\{-11, 11 \Big\} \\ -----------------\)
- \(-8x^2-200=0 \\
\Leftrightarrow -8x^2 = 200 \\
\Leftrightarrow x^2 = \frac{200}{-8} < 0 \\
V = \varnothing \\ -----------------\)
- \(9x^2-6=7x^2-6 \\ \Leftrightarrow 9x^2-7x^2=-6+6 \\
\Leftrightarrow 2x^2 = 0 \\
\Leftrightarrow x^2 = \frac{0}{2}\\
\Leftrightarrow x = 0 \\
V = \Big\{ 0 \Big\} \\ -----------------\)
- \(-10x^2+187=-6x^2-9 \\ \Leftrightarrow -10x^2+6x^2=-9-187 \\
\Leftrightarrow -4x^2 = -196 \\
\Leftrightarrow x^2 = \frac{-196}{-4}=49 \\
\Leftrightarrow x = 7 \vee x = -7 \\
V = \Big\{-7, 7 \Big\} \\ -----------------\)
- \(2x^2-338=0 \\
\Leftrightarrow 2x^2 = 338 \\
\Leftrightarrow x^2 = \frac{338}{2}=169 \\
\Leftrightarrow x = 13 \vee x = -13 \\
V = \Big\{-13, 13 \Big\} \\ -----------------\)
- \(11x^2-12=9x^2-4 \\ \Leftrightarrow 11x^2-9x^2=-4+12 \\
\Leftrightarrow 2x^2 = 8 \\
\Leftrightarrow x^2 = \frac{8}{2}=4 \\
\Leftrightarrow x = 2 \vee x = -2 \\
V = \Big\{-2, 2 \Big\} \\ -----------------\)