Los de vierkantsvergelijking op zonder de discriminant te gebruiken
- \(-3(-4x^2-8)=-(-14x^2-42)\)
- \(-3x^2+363=0\)
- \(-4(5x^2-7)=-(24x^2-28)\)
- \(12x^2-155=9x^2-8\)
- \(-2(8x^2-4)=-(19x^2-596)\)
- \(-7x^2-847=0\)
- \(5(7x^2+4)=-(-37x^2+268)\)
- \(-7x^2+1=-4x^2+4\)
- \(-3x^2+27=0\)
- \(6x^2-216=0\)
- \(-2(10x^2-3)=-(24x^2-582)\)
- \(12x^2+314=8x^2-10\)
Los de vierkantsvergelijking op zonder de discriminant te gebruiken
Verbetersleutel
- \(-3(-4x^2-8)=-(-14x^2-42) \\ \Leftrightarrow 12x^2+24=14x^2+42 \\
\Leftrightarrow 12x^2-14x^2=42-24 \\
\Leftrightarrow -2x^2 = 18 \\
\Leftrightarrow x^2 = \frac{18}{-2} < 0 \\
V = \varnothing \\ -----------------\)
- \(-3x^2+363=0 \\
\Leftrightarrow -3x^2 = -363 \\
\Leftrightarrow x^2 = \frac{-363}{-3}=121 \\
\Leftrightarrow x = 11 \vee x = -11 \\
V = \Big\{-11, 11 \Big\} \\ -----------------\)
- \(-4(5x^2-7)=-(24x^2-28) \\ \Leftrightarrow -20x^2+28=-24x^2+28 \\
\Leftrightarrow -20x^2+24x^2=28-28 \\
\Leftrightarrow 4x^2 = 0 \\
\Leftrightarrow x^2 = \frac{0}{4}\\
\Leftrightarrow x = 0 \\
V = \Big\{ 0 \Big\} \\ -----------------\)
- \(12x^2-155=9x^2-8 \\ \Leftrightarrow 12x^2-9x^2=-8+155 \\
\Leftrightarrow 3x^2 = 147 \\
\Leftrightarrow x^2 = \frac{147}{3}=49 \\
\Leftrightarrow x = 7 \vee x = -7 \\
V = \Big\{-7, 7 \Big\} \\ -----------------\)
- \(-2(8x^2-4)=-(19x^2-596) \\ \Leftrightarrow -16x^2+8=-19x^2+596 \\
\Leftrightarrow -16x^2+19x^2=596-8 \\
\Leftrightarrow 3x^2 = 588 \\
\Leftrightarrow x^2 = \frac{588}{3}=196 \\
\Leftrightarrow x = 14 \vee x = -14 \\
V = \Big\{-14, 14 \Big\} \\ -----------------\)
- \(-7x^2-847=0 \\
\Leftrightarrow -7x^2 = 847 \\
\Leftrightarrow x^2 = \frac{847}{-7} < 0 \\
V = \varnothing \\ -----------------\)
- \(5(7x^2+4)=-(-37x^2+268) \\ \Leftrightarrow 35x^2+20=37x^2-268 \\
\Leftrightarrow 35x^2-37x^2=-268-20 \\
\Leftrightarrow -2x^2 = -288 \\
\Leftrightarrow x^2 = \frac{-288}{-2}=144 \\
\Leftrightarrow x = 12 \vee x = -12 \\
V = \Big\{-12, 12 \Big\} \\ -----------------\)
- \(-7x^2+1=-4x^2+4 \\ \Leftrightarrow -7x^2+4x^2=4-1 \\
\Leftrightarrow -3x^2 = 3 \\
\Leftrightarrow x^2 = \frac{3}{-3} < 0 \\
V = \varnothing \\ -----------------\)
- \(-3x^2+27=0 \\
\Leftrightarrow -3x^2 = -27 \\
\Leftrightarrow x^2 = \frac{-27}{-3}=9 \\
\Leftrightarrow x = 3 \vee x = -3 \\
V = \Big\{-3, 3 \Big\} \\ -----------------\)
- \(6x^2-216=0 \\
\Leftrightarrow 6x^2 = 216 \\
\Leftrightarrow x^2 = \frac{216}{6}=36 \\
\Leftrightarrow x = 6 \vee x = -6 \\
V = \Big\{-6, 6 \Big\} \\ -----------------\)
- \(-2(10x^2-3)=-(24x^2-582) \\ \Leftrightarrow -20x^2+6=-24x^2+582 \\
\Leftrightarrow -20x^2+24x^2=582-6 \\
\Leftrightarrow 4x^2 = 576 \\
\Leftrightarrow x^2 = \frac{576}{4}=144 \\
\Leftrightarrow x = 12 \vee x = -12 \\
V = \Big\{-12, 12 \Big\} \\ -----------------\)
- \(12x^2+314=8x^2-10 \\ \Leftrightarrow 12x^2-8x^2=-10-314 \\
\Leftrightarrow 4x^2 = -324 \\
\Leftrightarrow x^2 = \frac{-324}{4} < 0 \\
V = \varnothing \\ -----------------\)