Los de vierkantsvergelijking op zonder de discriminant te gebruiken
- \(-5x^2-980=0\)
- \(-4(9x^2-6)=-(32x^2+40)\)
- \(-3(-9x^2+5)=-(-19x^2+143)\)
- \(-5(-8x^2+8)=-(-43x^2+40)\)
- \(8x^2+0=0\)
- \(6x^2-10=4x^2+8\)
- \(-12x^2-188=-7x^2-8\)
- \(-9x^2+376=-3x^2-8\)
- \(4(7x^2-10)=-(-30x^2+168)\)
- \(3x^2-363=0\)
- \(-6x^2+172=-4x^2+10\)
- \(-5(4x^2+7)=-(25x^2+15)\)
Los de vierkantsvergelijking op zonder de discriminant te gebruiken
Verbetersleutel
- \(-5x^2-980=0 \\
\Leftrightarrow -5x^2 = 980 \\
\Leftrightarrow x^2 = \frac{980}{-5} < 0 \\
V = \varnothing \\ -----------------\)
- \(-4(9x^2-6)=-(32x^2+40) \\ \Leftrightarrow -36x^2+24=-32x^2-40 \\
\Leftrightarrow -36x^2+32x^2=-40-24 \\
\Leftrightarrow -4x^2 = -64 \\
\Leftrightarrow x^2 = \frac{-64}{-4}=16 \\
\Leftrightarrow x = 4 \vee x = -4 \\
V = \Big\{-4, 4 \Big\} \\ -----------------\)
- \(-3(-9x^2+5)=-(-19x^2+143) \\ \Leftrightarrow 27x^2-15=19x^2-143 \\
\Leftrightarrow 27x^2-19x^2=-143+15 \\
\Leftrightarrow 8x^2 = -128 \\
\Leftrightarrow x^2 = \frac{-128}{8} < 0 \\
V = \varnothing \\ -----------------\)
- \(-5(-8x^2+8)=-(-43x^2+40) \\ \Leftrightarrow 40x^2-40=43x^2-40 \\
\Leftrightarrow 40x^2-43x^2=-40+40 \\
\Leftrightarrow -3x^2 = 0 \\
\Leftrightarrow x^2 = \frac{0}{-3}\\
\Leftrightarrow x = 0 \\
V = \Big\{ 0 \Big\} \\ -----------------\)
- \(8x^2+0=0 \\
\Leftrightarrow 8x^2 = 0 \\
\Leftrightarrow x^2 = \frac{0}{8}\\
\Leftrightarrow x = 0 \\
V = \Big\{ 0 \Big\} \\ -----------------\)
- \(6x^2-10=4x^2+8 \\ \Leftrightarrow 6x^2-4x^2=8+10 \\
\Leftrightarrow 2x^2 = 18 \\
\Leftrightarrow x^2 = \frac{18}{2}=9 \\
\Leftrightarrow x = 3 \vee x = -3 \\
V = \Big\{-3, 3 \Big\} \\ -----------------\)
- \(-12x^2-188=-7x^2-8 \\ \Leftrightarrow -12x^2+7x^2=-8+188 \\
\Leftrightarrow -5x^2 = 180 \\
\Leftrightarrow x^2 = \frac{180}{-5} < 0 \\
V = \varnothing \\ -----------------\)
- \(-9x^2+376=-3x^2-8 \\ \Leftrightarrow -9x^2+3x^2=-8-376 \\
\Leftrightarrow -6x^2 = -384 \\
\Leftrightarrow x^2 = \frac{-384}{-6}=64 \\
\Leftrightarrow x = 8 \vee x = -8 \\
V = \Big\{-8, 8 \Big\} \\ -----------------\)
- \(4(7x^2-10)=-(-30x^2+168) \\ \Leftrightarrow 28x^2-40=30x^2-168 \\
\Leftrightarrow 28x^2-30x^2=-168+40 \\
\Leftrightarrow -2x^2 = -128 \\
\Leftrightarrow x^2 = \frac{-128}{-2}=64 \\
\Leftrightarrow x = 8 \vee x = -8 \\
V = \Big\{-8, 8 \Big\} \\ -----------------\)
- \(3x^2-363=0 \\
\Leftrightarrow 3x^2 = 363 \\
\Leftrightarrow x^2 = \frac{363}{3}=121 \\
\Leftrightarrow x = 11 \vee x = -11 \\
V = \Big\{-11, 11 \Big\} \\ -----------------\)
- \(-6x^2+172=-4x^2+10 \\ \Leftrightarrow -6x^2+4x^2=10-172 \\
\Leftrightarrow -2x^2 = -162 \\
\Leftrightarrow x^2 = \frac{-162}{-2}=81 \\
\Leftrightarrow x = 9 \vee x = -9 \\
V = \Big\{-9, 9 \Big\} \\ -----------------\)
- \(-5(4x^2+7)=-(25x^2+15) \\ \Leftrightarrow -20x^2-35=-25x^2-15 \\
\Leftrightarrow -20x^2+25x^2=-15+35 \\
\Leftrightarrow 5x^2 = 20 \\
\Leftrightarrow x^2 = \frac{20}{5}=4 \\
\Leftrightarrow x = 2 \vee x = -2 \\
V = \Big\{-2, 2 \Big\} \\ -----------------\)