Los de vierkantsvergelijking op zonder de discriminant te gebruiken
- \(-2x^2+51=-5x^2+3\)
- \(4(10x^2-3)=-(-48x^2+300)\)
- \(4x^2-64=0\)
- \(-3x^2+8=-2x^2+8\)
- \(-2x^2-242=0\)
- \(-5x^2+720=0\)
- \(-2x^2-162=0\)
- \(-11x^2+696=-4x^2-4\)
- \(-4(-3x^2+9)=-(-17x^2+36)\)
- \(6x^2-1176=0\)
- \(3(-4x^2+6)=-(15x^2-606)\)
- \(4x^2-324=0\)
Los de vierkantsvergelijking op zonder de discriminant te gebruiken
Verbetersleutel
- \(-2x^2+51=-5x^2+3 \\ \Leftrightarrow -2x^2+5x^2=3-51 \\
\Leftrightarrow 3x^2 = -48 \\
\Leftrightarrow x^2 = \frac{-48}{3} < 0 \\
V = \varnothing \\ -----------------\)
- \(4(10x^2-3)=-(-48x^2+300) \\ \Leftrightarrow 40x^2-12=48x^2-300 \\
\Leftrightarrow 40x^2-48x^2=-300+12 \\
\Leftrightarrow -8x^2 = -288 \\
\Leftrightarrow x^2 = \frac{-288}{-8}=36 \\
\Leftrightarrow x = 6 \vee x = -6 \\
V = \Big\{-6, 6 \Big\} \\ -----------------\)
- \(4x^2-64=0 \\
\Leftrightarrow 4x^2 = 64 \\
\Leftrightarrow x^2 = \frac{64}{4}=16 \\
\Leftrightarrow x = 4 \vee x = -4 \\
V = \Big\{-4, 4 \Big\} \\ -----------------\)
- \(-3x^2+8=-2x^2+8 \\ \Leftrightarrow -3x^2+2x^2=8-8 \\
\Leftrightarrow -x^2 = 0 \\
\Leftrightarrow x^2 = \frac{0}{-1}\\
\Leftrightarrow x = 0 \\
V = \Big\{ 0 \Big\} \\ -----------------\)
- \(-2x^2-242=0 \\
\Leftrightarrow -2x^2 = 242 \\
\Leftrightarrow x^2 = \frac{242}{-2} < 0 \\
V = \varnothing \\ -----------------\)
- \(-5x^2+720=0 \\
\Leftrightarrow -5x^2 = -720 \\
\Leftrightarrow x^2 = \frac{-720}{-5}=144 \\
\Leftrightarrow x = 12 \vee x = -12 \\
V = \Big\{-12, 12 \Big\} \\ -----------------\)
- \(-2x^2-162=0 \\
\Leftrightarrow -2x^2 = 162 \\
\Leftrightarrow x^2 = \frac{162}{-2} < 0 \\
V = \varnothing \\ -----------------\)
- \(-11x^2+696=-4x^2-4 \\ \Leftrightarrow -11x^2+4x^2=-4-696 \\
\Leftrightarrow -7x^2 = -700 \\
\Leftrightarrow x^2 = \frac{-700}{-7}=100 \\
\Leftrightarrow x = 10 \vee x = -10 \\
V = \Big\{-10, 10 \Big\} \\ -----------------\)
- \(-4(-3x^2+9)=-(-17x^2+36) \\ \Leftrightarrow 12x^2-36=17x^2-36 \\
\Leftrightarrow 12x^2-17x^2=-36+36 \\
\Leftrightarrow -5x^2 = 0 \\
\Leftrightarrow x^2 = \frac{0}{-5}\\
\Leftrightarrow x = 0 \\
V = \Big\{ 0 \Big\} \\ -----------------\)
- \(6x^2-1176=0 \\
\Leftrightarrow 6x^2 = 1176 \\
\Leftrightarrow x^2 = \frac{1176}{6}=196 \\
\Leftrightarrow x = 14 \vee x = -14 \\
V = \Big\{-14, 14 \Big\} \\ -----------------\)
- \(3(-4x^2+6)=-(15x^2-606) \\ \Leftrightarrow -12x^2+18=-15x^2+606 \\
\Leftrightarrow -12x^2+15x^2=606-18 \\
\Leftrightarrow 3x^2 = 588 \\
\Leftrightarrow x^2 = \frac{588}{3}=196 \\
\Leftrightarrow x = 14 \vee x = -14 \\
V = \Big\{-14, 14 \Big\} \\ -----------------\)
- \(4x^2-324=0 \\
\Leftrightarrow 4x^2 = 324 \\
\Leftrightarrow x^2 = \frac{324}{4}=81 \\
\Leftrightarrow x = 9 \vee x = -9 \\
V = \Big\{-9, 9 \Big\} \\ -----------------\)