Los de vierkantsvergelijking op zonder de discriminant te gebruiken
- \(-8x^2+200=0\)
- \(-2x^2-7=-7x^2-2\)
- \(3(-7x^2+6)=-(24x^2-30)\)
- \(-17x^2+1573=-9x^2+5\)
- \(-5(-3x^2+2)=-(-22x^2+577)\)
- \(3x^2-363=0\)
- \(-11x^2-73=-7x^2-9\)
- \(-5(-3x^2+2)=-(-11x^2-186)\)
- \(-7x^2+175=0\)
- \(4(8x^2+7)=-(-27x^2-153)\)
- \(4x^2-7=-2x^2-7\)
- \(3x^2+0=0\)
Los de vierkantsvergelijking op zonder de discriminant te gebruiken
Verbetersleutel
- \(-8x^2+200=0 \\
\Leftrightarrow -8x^2 = -200 \\
\Leftrightarrow x^2 = \frac{-200}{-8}=25 \\
\Leftrightarrow x = 5 \vee x = -5 \\
V = \Big\{-5, 5 \Big\} \\ -----------------\)
- \(-2x^2-7=-7x^2-2 \\ \Leftrightarrow -2x^2+7x^2=-2+7 \\
\Leftrightarrow 5x^2 = 5 \\
\Leftrightarrow x^2 = \frac{5}{5}=1 \\
\Leftrightarrow x = 1 \vee x = -1 \\
V = \Big\{-1, 1 \Big\} \\ -----------------\)
- \(3(-7x^2+6)=-(24x^2-30) \\ \Leftrightarrow -21x^2+18=-24x^2+30 \\
\Leftrightarrow -21x^2+24x^2=30-18 \\
\Leftrightarrow 3x^2 = 12 \\
\Leftrightarrow x^2 = \frac{12}{3}=4 \\
\Leftrightarrow x = 2 \vee x = -2 \\
V = \Big\{-2, 2 \Big\} \\ -----------------\)
- \(-17x^2+1573=-9x^2+5 \\ \Leftrightarrow -17x^2+9x^2=5-1573 \\
\Leftrightarrow -8x^2 = -1568 \\
\Leftrightarrow x^2 = \frac{-1568}{-8}=196 \\
\Leftrightarrow x = 14 \vee x = -14 \\
V = \Big\{-14, 14 \Big\} \\ -----------------\)
- \(-5(-3x^2+2)=-(-22x^2+577) \\ \Leftrightarrow 15x^2-10=22x^2-577 \\
\Leftrightarrow 15x^2-22x^2=-577+10 \\
\Leftrightarrow -7x^2 = -567 \\
\Leftrightarrow x^2 = \frac{-567}{-7}=81 \\
\Leftrightarrow x = 9 \vee x = -9 \\
V = \Big\{-9, 9 \Big\} \\ -----------------\)
- \(3x^2-363=0 \\
\Leftrightarrow 3x^2 = 363 \\
\Leftrightarrow x^2 = \frac{363}{3}=121 \\
\Leftrightarrow x = 11 \vee x = -11 \\
V = \Big\{-11, 11 \Big\} \\ -----------------\)
- \(-11x^2-73=-7x^2-9 \\ \Leftrightarrow -11x^2+7x^2=-9+73 \\
\Leftrightarrow -4x^2 = 64 \\
\Leftrightarrow x^2 = \frac{64}{-4} < 0 \\
V = \varnothing \\ -----------------\)
- \(-5(-3x^2+2)=-(-11x^2-186) \\ \Leftrightarrow 15x^2-10=11x^2+186 \\
\Leftrightarrow 15x^2-11x^2=186+10 \\
\Leftrightarrow 4x^2 = 196 \\
\Leftrightarrow x^2 = \frac{196}{4}=49 \\
\Leftrightarrow x = 7 \vee x = -7 \\
V = \Big\{-7, 7 \Big\} \\ -----------------\)
- \(-7x^2+175=0 \\
\Leftrightarrow -7x^2 = -175 \\
\Leftrightarrow x^2 = \frac{-175}{-7}=25 \\
\Leftrightarrow x = 5 \vee x = -5 \\
V = \Big\{-5, 5 \Big\} \\ -----------------\)
- \(4(8x^2+7)=-(-27x^2-153) \\ \Leftrightarrow 32x^2+28=27x^2+153 \\
\Leftrightarrow 32x^2-27x^2=153-28 \\
\Leftrightarrow 5x^2 = 125 \\
\Leftrightarrow x^2 = \frac{125}{5}=25 \\
\Leftrightarrow x = 5 \vee x = -5 \\
V = \Big\{-5, 5 \Big\} \\ -----------------\)
- \(4x^2-7=-2x^2-7 \\ \Leftrightarrow 4x^2+2x^2=-7+7 \\
\Leftrightarrow 6x^2 = 0 \\
\Leftrightarrow x^2 = \frac{0}{6}\\
\Leftrightarrow x = 0 \\
V = \Big\{ 0 \Big\} \\ -----------------\)
- \(3x^2+0=0 \\
\Leftrightarrow 3x^2 = 0 \\
\Leftrightarrow x^2 = \frac{0}{3}\\
\Leftrightarrow x = 0 \\
V = \Big\{ 0 \Big\} \\ -----------------\)