Los de vierkantsvergelijking op zonder de discriminant te gebruiken
- \(2(3x^2-4)=-(-7x^2+8)\)
- \(-6x^2-726=0\)
- \(-10x^2+905=-6x^2+5\)
- \(-6x^2+486=0\)
- \(4x^2-484=0\)
- \(2(-9x^2-3)=-(23x^2-39)\)
- \(5x^2-389=-3x^2+3\)
- \(5(10x^2+10)=-(-45x^2-55)\)
- \(13x^2-290=5x^2-2\)
- \(-2(10x^2+10)=-(19x^2+101)\)
- \(-2x^2+206=6x^2+6\)
- \(3x^2+21=9x^2-3\)
Los de vierkantsvergelijking op zonder de discriminant te gebruiken
Verbetersleutel
- \(2(3x^2-4)=-(-7x^2+8) \\ \Leftrightarrow 6x^2-8=7x^2-8 \\
\Leftrightarrow 6x^2-7x^2=-8+8 \\
\Leftrightarrow -x^2 = 0 \\
\Leftrightarrow x^2 = \frac{0}{-1}\\
\Leftrightarrow x = 0 \\
V = \Big\{ 0 \Big\} \\ -----------------\)
- \(-6x^2-726=0 \\
\Leftrightarrow -6x^2 = 726 \\
\Leftrightarrow x^2 = \frac{726}{-6} < 0 \\
V = \varnothing \\ -----------------\)
- \(-10x^2+905=-6x^2+5 \\ \Leftrightarrow -10x^2+6x^2=5-905 \\
\Leftrightarrow -4x^2 = -900 \\
\Leftrightarrow x^2 = \frac{-900}{-4}=225 \\
\Leftrightarrow x = 15 \vee x = -15 \\
V = \Big\{-15, 15 \Big\} \\ -----------------\)
- \(-6x^2+486=0 \\
\Leftrightarrow -6x^2 = -486 \\
\Leftrightarrow x^2 = \frac{-486}{-6}=81 \\
\Leftrightarrow x = 9 \vee x = -9 \\
V = \Big\{-9, 9 \Big\} \\ -----------------\)
- \(4x^2-484=0 \\
\Leftrightarrow 4x^2 = 484 \\
\Leftrightarrow x^2 = \frac{484}{4}=121 \\
\Leftrightarrow x = 11 \vee x = -11 \\
V = \Big\{-11, 11 \Big\} \\ -----------------\)
- \(2(-9x^2-3)=-(23x^2-39) \\ \Leftrightarrow -18x^2-6=-23x^2+39 \\
\Leftrightarrow -18x^2+23x^2=39+6 \\
\Leftrightarrow 5x^2 = 45 \\
\Leftrightarrow x^2 = \frac{45}{5}=9 \\
\Leftrightarrow x = 3 \vee x = -3 \\
V = \Big\{-3, 3 \Big\} \\ -----------------\)
- \(5x^2-389=-3x^2+3 \\ \Leftrightarrow 5x^2+3x^2=3+389 \\
\Leftrightarrow 8x^2 = 392 \\
\Leftrightarrow x^2 = \frac{392}{8}=49 \\
\Leftrightarrow x = 7 \vee x = -7 \\
V = \Big\{-7, 7 \Big\} \\ -----------------\)
- \(5(10x^2+10)=-(-45x^2-55) \\ \Leftrightarrow 50x^2+50=45x^2+55 \\
\Leftrightarrow 50x^2-45x^2=55-50 \\
\Leftrightarrow 5x^2 = 5 \\
\Leftrightarrow x^2 = \frac{5}{5}=1 \\
\Leftrightarrow x = 1 \vee x = -1 \\
V = \Big\{-1, 1 \Big\} \\ -----------------\)
- \(13x^2-290=5x^2-2 \\ \Leftrightarrow 13x^2-5x^2=-2+290 \\
\Leftrightarrow 8x^2 = 288 \\
\Leftrightarrow x^2 = \frac{288}{8}=36 \\
\Leftrightarrow x = 6 \vee x = -6 \\
V = \Big\{-6, 6 \Big\} \\ -----------------\)
- \(-2(10x^2+10)=-(19x^2+101) \\ \Leftrightarrow -20x^2-20=-19x^2-101 \\
\Leftrightarrow -20x^2+19x^2=-101+20 \\
\Leftrightarrow -x^2 = -81 \\
\Leftrightarrow x^2 = \frac{-81}{-1}=81 \\
\Leftrightarrow x = 9 \vee x = -9 \\
V = \Big\{-9, 9 \Big\} \\ -----------------\)
- \(-2x^2+206=6x^2+6 \\ \Leftrightarrow -2x^2-6x^2=6-206 \\
\Leftrightarrow -8x^2 = -200 \\
\Leftrightarrow x^2 = \frac{-200}{-8}=25 \\
\Leftrightarrow x = 5 \vee x = -5 \\
V = \Big\{-5, 5 \Big\} \\ -----------------\)
- \(3x^2+21=9x^2-3 \\ \Leftrightarrow 3x^2-9x^2=-3-21 \\
\Leftrightarrow -6x^2 = -24 \\
\Leftrightarrow x^2 = \frac{-24}{-6}=4 \\
\Leftrightarrow x = 2 \vee x = -2 \\
V = \Big\{-2, 2 \Big\} \\ -----------------\)