Los de vierkantsvergelijking op zonder de discriminant te gebruiken
- \(2(2x^2-6)=-(-12x^2+812)\)
- \(-5(-3x^2-6)=-(-17x^2-272)\)
- \(5x^2+10=9x^2+10\)
- \(-8x^2+512=0\)
- \(x^2-1=0\)
- \(2(5x^2+7)=-(-6x^2-270)\)
- \(7x^2-7=0\)
- \(3x^2-477=9x^2+9\)
- \(2x^2-18=0\)
- \(-3x^2+27=0\)
- \(-3(-8x^2+10)=-(-26x^2-362)\)
- \(3(-2x^2+4)=-(9x^2-120)\)
Los de vierkantsvergelijking op zonder de discriminant te gebruiken
Verbetersleutel
- \(2(2x^2-6)=-(-12x^2+812) \\ \Leftrightarrow 4x^2-12=12x^2-812 \\
\Leftrightarrow 4x^2-12x^2=-812+12 \\
\Leftrightarrow -8x^2 = -800 \\
\Leftrightarrow x^2 = \frac{-800}{-8}=100 \\
\Leftrightarrow x = 10 \vee x = -10 \\
V = \Big\{-10, 10 \Big\} \\ -----------------\)
- \(-5(-3x^2-6)=-(-17x^2-272) \\ \Leftrightarrow 15x^2+30=17x^2+272 \\
\Leftrightarrow 15x^2-17x^2=272-30 \\
\Leftrightarrow -2x^2 = 242 \\
\Leftrightarrow x^2 = \frac{242}{-2} < 0 \\
V = \varnothing \\ -----------------\)
- \(5x^2+10=9x^2+10 \\ \Leftrightarrow 5x^2-9x^2=10-10 \\
\Leftrightarrow -4x^2 = 0 \\
\Leftrightarrow x^2 = \frac{0}{-4}\\
\Leftrightarrow x = 0 \\
V = \Big\{ 0 \Big\} \\ -----------------\)
- \(-8x^2+512=0 \\
\Leftrightarrow -8x^2 = -512 \\
\Leftrightarrow x^2 = \frac{-512}{-8}=64 \\
\Leftrightarrow x = 8 \vee x = -8 \\
V = \Big\{-8, 8 \Big\} \\ -----------------\)
- \(x^2-1=0 \\
\Leftrightarrow x^2 = 1 \\
\Leftrightarrow x^2 = \frac{1}{1}=1 \\
\Leftrightarrow x = 1 \vee x = -1 \\
V = \Big\{-1, 1 \Big\} \\ -----------------\)
- \(2(5x^2+7)=-(-6x^2-270) \\ \Leftrightarrow 10x^2+14=6x^2+270 \\
\Leftrightarrow 10x^2-6x^2=270-14 \\
\Leftrightarrow 4x^2 = 256 \\
\Leftrightarrow x^2 = \frac{256}{4}=64 \\
\Leftrightarrow x = 8 \vee x = -8 \\
V = \Big\{-8, 8 \Big\} \\ -----------------\)
- \(7x^2-7=0 \\
\Leftrightarrow 7x^2 = 7 \\
\Leftrightarrow x^2 = \frac{7}{7}=1 \\
\Leftrightarrow x = 1 \vee x = -1 \\
V = \Big\{-1, 1 \Big\} \\ -----------------\)
- \(3x^2-477=9x^2+9 \\ \Leftrightarrow 3x^2-9x^2=9+477 \\
\Leftrightarrow -6x^2 = 486 \\
\Leftrightarrow x^2 = \frac{486}{-6} < 0 \\
V = \varnothing \\ -----------------\)
- \(2x^2-18=0 \\
\Leftrightarrow 2x^2 = 18 \\
\Leftrightarrow x^2 = \frac{18}{2}=9 \\
\Leftrightarrow x = 3 \vee x = -3 \\
V = \Big\{-3, 3 \Big\} \\ -----------------\)
- \(-3x^2+27=0 \\
\Leftrightarrow -3x^2 = -27 \\
\Leftrightarrow x^2 = \frac{-27}{-3}=9 \\
\Leftrightarrow x = 3 \vee x = -3 \\
V = \Big\{-3, 3 \Big\} \\ -----------------\)
- \(-3(-8x^2+10)=-(-26x^2-362) \\ \Leftrightarrow 24x^2-30=26x^2+362 \\
\Leftrightarrow 24x^2-26x^2=362+30 \\
\Leftrightarrow -2x^2 = 392 \\
\Leftrightarrow x^2 = \frac{392}{-2} < 0 \\
V = \varnothing \\ -----------------\)
- \(3(-2x^2+4)=-(9x^2-120) \\ \Leftrightarrow -6x^2+12=-9x^2+120 \\
\Leftrightarrow -6x^2+9x^2=120-12 \\
\Leftrightarrow 3x^2 = 108 \\
\Leftrightarrow x^2 = \frac{108}{3}=36 \\
\Leftrightarrow x = 6 \vee x = -6 \\
V = \Big\{-6, 6 \Big\} \\ -----------------\)