Los de vierkantsvergelijking op zonder de discriminant te gebruiken
- \(-4x^2-597=-7x^2-9\)
- \(2(3x^2-8)=-(-14x^2+1368)\)
- \(-7x^2+700=0\)
- \(4(-6x^2-2)=-(25x^2-17)\)
- \(6x^2+295=9x^2-5\)
- \(-2x^2+19=-5x^2-8\)
- \(-3(2x^2+6)=-(x^2+23)\)
- \(-10x^2-404=-6x^2-4\)
- \(8x^2+968=0\)
- \(-3x^2+4=-8x^2+4\)
- \(-5(-4x^2+5)=-(-25x^2+525)\)
- \(8x^2-512=0\)
Los de vierkantsvergelijking op zonder de discriminant te gebruiken
Verbetersleutel
- \(-4x^2-597=-7x^2-9 \\ \Leftrightarrow -4x^2+7x^2=-9+597 \\
\Leftrightarrow 3x^2 = 588 \\
\Leftrightarrow x^2 = \frac{588}{3}=196 \\
\Leftrightarrow x = 14 \vee x = -14 \\
V = \Big\{-14, 14 \Big\} \\ -----------------\)
- \(2(3x^2-8)=-(-14x^2+1368) \\ \Leftrightarrow 6x^2-16=14x^2-1368 \\
\Leftrightarrow 6x^2-14x^2=-1368+16 \\
\Leftrightarrow -8x^2 = -1352 \\
\Leftrightarrow x^2 = \frac{-1352}{-8}=169 \\
\Leftrightarrow x = 13 \vee x = -13 \\
V = \Big\{-13, 13 \Big\} \\ -----------------\)
- \(-7x^2+700=0 \\
\Leftrightarrow -7x^2 = -700 \\
\Leftrightarrow x^2 = \frac{-700}{-7}=100 \\
\Leftrightarrow x = 10 \vee x = -10 \\
V = \Big\{-10, 10 \Big\} \\ -----------------\)
- \(4(-6x^2-2)=-(25x^2-17) \\ \Leftrightarrow -24x^2-8=-25x^2+17 \\
\Leftrightarrow -24x^2+25x^2=17+8 \\
\Leftrightarrow x^2 = 25 \\
\Leftrightarrow x^2 = \frac{25}{1}=25 \\
\Leftrightarrow x = 5 \vee x = -5 \\
V = \Big\{-5, 5 \Big\} \\ -----------------\)
- \(6x^2+295=9x^2-5 \\ \Leftrightarrow 6x^2-9x^2=-5-295 \\
\Leftrightarrow -3x^2 = -300 \\
\Leftrightarrow x^2 = \frac{-300}{-3}=100 \\
\Leftrightarrow x = 10 \vee x = -10 \\
V = \Big\{-10, 10 \Big\} \\ -----------------\)
- \(-2x^2+19=-5x^2-8 \\ \Leftrightarrow -2x^2+5x^2=-8-19 \\
\Leftrightarrow 3x^2 = -27 \\
\Leftrightarrow x^2 = \frac{-27}{3} < 0 \\
V = \varnothing \\ -----------------\)
- \(-3(2x^2+6)=-(x^2+23) \\ \Leftrightarrow -6x^2-18=-x^2-23 \\
\Leftrightarrow -6x^2+x^2=-23+18 \\
\Leftrightarrow -5x^2 = -5 \\
\Leftrightarrow x^2 = \frac{-5}{-5}=1 \\
\Leftrightarrow x = 1 \vee x = -1 \\
V = \Big\{-1, 1 \Big\} \\ -----------------\)
- \(-10x^2-404=-6x^2-4 \\ \Leftrightarrow -10x^2+6x^2=-4+404 \\
\Leftrightarrow -4x^2 = 400 \\
\Leftrightarrow x^2 = \frac{400}{-4} < 0 \\
V = \varnothing \\ -----------------\)
- \(8x^2+968=0 \\
\Leftrightarrow 8x^2 = -968 \\
\Leftrightarrow x^2 = \frac{-968}{8} < 0 \\
V = \varnothing \\ -----------------\)
- \(-3x^2+4=-8x^2+4 \\ \Leftrightarrow -3x^2+8x^2=4-4 \\
\Leftrightarrow 5x^2 = 0 \\
\Leftrightarrow x^2 = \frac{0}{5}\\
\Leftrightarrow x = 0 \\
V = \Big\{ 0 \Big\} \\ -----------------\)
- \(-5(-4x^2+5)=-(-25x^2+525) \\ \Leftrightarrow 20x^2-25=25x^2-525 \\
\Leftrightarrow 20x^2-25x^2=-525+25 \\
\Leftrightarrow -5x^2 = -500 \\
\Leftrightarrow x^2 = \frac{-500}{-5}=100 \\
\Leftrightarrow x = 10 \vee x = -10 \\
V = \Big\{-10, 10 \Big\} \\ -----------------\)
- \(8x^2-512=0 \\
\Leftrightarrow 8x^2 = 512 \\
\Leftrightarrow x^2 = \frac{512}{8}=64 \\
\Leftrightarrow x = 8 \vee x = -8 \\
V = \Big\{-8, 8 \Big\} \\ -----------------\)