Los de vierkantsvergelijking op zonder de discriminant te gebruiken
- \(4x^2+900=0\)
- \(4x^2+19=-2x^2-5\)
- \(-7x^2-700=0\)
- \(-4x^2+484=0\)
- \(-4(-6x^2-3)=-(-25x^2-181)\)
- \(-5x^2-42=-4x^2-6\)
- \(3x^2-182=10x^2-7\)
- \(-8x^2+0=0\)
- \(-3x^2+810=5x^2+10\)
- \(-5x^2+845=0\)
- \(7x^2+77=9x^2+5\)
- \(2x^2-2=5x^2-5\)
Los de vierkantsvergelijking op zonder de discriminant te gebruiken
Verbetersleutel
- \(4x^2+900=0 \\
\Leftrightarrow 4x^2 = -900 \\
\Leftrightarrow x^2 = \frac{-900}{4} < 0 \\
V = \varnothing \\ -----------------\)
- \(4x^2+19=-2x^2-5 \\ \Leftrightarrow 4x^2+2x^2=-5-19 \\
\Leftrightarrow 6x^2 = -24 \\
\Leftrightarrow x^2 = \frac{-24}{6} < 0 \\
V = \varnothing \\ -----------------\)
- \(-7x^2-700=0 \\
\Leftrightarrow -7x^2 = 700 \\
\Leftrightarrow x^2 = \frac{700}{-7} < 0 \\
V = \varnothing \\ -----------------\)
- \(-4x^2+484=0 \\
\Leftrightarrow -4x^2 = -484 \\
\Leftrightarrow x^2 = \frac{-484}{-4}=121 \\
\Leftrightarrow x = 11 \vee x = -11 \\
V = \Big\{-11, 11 \Big\} \\ -----------------\)
- \(-4(-6x^2-3)=-(-25x^2-181) \\ \Leftrightarrow 24x^2+12=25x^2+181 \\
\Leftrightarrow 24x^2-25x^2=181-12 \\
\Leftrightarrow -x^2 = 169 \\
\Leftrightarrow x^2 = \frac{169}{-1} < 0 \\
V = \varnothing \\ -----------------\)
- \(-5x^2-42=-4x^2-6 \\ \Leftrightarrow -5x^2+4x^2=-6+42 \\
\Leftrightarrow -x^2 = 36 \\
\Leftrightarrow x^2 = \frac{36}{-1} < 0 \\
V = \varnothing \\ -----------------\)
- \(3x^2-182=10x^2-7 \\ \Leftrightarrow 3x^2-10x^2=-7+182 \\
\Leftrightarrow -7x^2 = 175 \\
\Leftrightarrow x^2 = \frac{175}{-7} < 0 \\
V = \varnothing \\ -----------------\)
- \(-8x^2+0=0 \\
\Leftrightarrow -8x^2 = 0 \\
\Leftrightarrow x^2 = \frac{0}{-8}\\
\Leftrightarrow x = 0 \\
V = \Big\{ 0 \Big\} \\ -----------------\)
- \(-3x^2+810=5x^2+10 \\ \Leftrightarrow -3x^2-5x^2=10-810 \\
\Leftrightarrow -8x^2 = -800 \\
\Leftrightarrow x^2 = \frac{-800}{-8}=100 \\
\Leftrightarrow x = 10 \vee x = -10 \\
V = \Big\{-10, 10 \Big\} \\ -----------------\)
- \(-5x^2+845=0 \\
\Leftrightarrow -5x^2 = -845 \\
\Leftrightarrow x^2 = \frac{-845}{-5}=169 \\
\Leftrightarrow x = 13 \vee x = -13 \\
V = \Big\{-13, 13 \Big\} \\ -----------------\)
- \(7x^2+77=9x^2+5 \\ \Leftrightarrow 7x^2-9x^2=5-77 \\
\Leftrightarrow -2x^2 = -72 \\
\Leftrightarrow x^2 = \frac{-72}{-2}=36 \\
\Leftrightarrow x = 6 \vee x = -6 \\
V = \Big\{-6, 6 \Big\} \\ -----------------\)
- \(2x^2-2=5x^2-5 \\ \Leftrightarrow 2x^2-5x^2=-5+2 \\
\Leftrightarrow -3x^2 = -3 \\
\Leftrightarrow x^2 = \frac{-3}{-3}=1 \\
\Leftrightarrow x = 1 \vee x = -1 \\
V = \Big\{-1, 1 \Big\} \\ -----------------\)