Los de vierkantsvergelijking op zonder de discriminant te gebruiken
- \(-5x^2+80=0\)
- \(5x^2+388=3x^2-4\)
- \(2(-5x^2-2)=-(2x^2-508)\)
- \(-x^2-64=0\)
- \(-3(4x^2-3)=-(14x^2-107)\)
- \(7x^2+63=0\)
- \(x^2+56=2x^2+7\)
- \(x^2+9=0\)
- \(4(7x^2+3)=-(-31x^2+15)\)
- \(5x^2-1125=0\)
- \(-3x^2+243=0\)
- \(6x^2-32=2x^2+4\)
Los de vierkantsvergelijking op zonder de discriminant te gebruiken
Verbetersleutel
- \(-5x^2+80=0 \\
\Leftrightarrow -5x^2 = -80 \\
\Leftrightarrow x^2 = \frac{-80}{-5}=16 \\
\Leftrightarrow x = 4 \vee x = -4 \\
V = \Big\{-4, 4 \Big\} \\ -----------------\)
- \(5x^2+388=3x^2-4 \\ \Leftrightarrow 5x^2-3x^2=-4-388 \\
\Leftrightarrow 2x^2 = -392 \\
\Leftrightarrow x^2 = \frac{-392}{2} < 0 \\
V = \varnothing \\ -----------------\)
- \(2(-5x^2-2)=-(2x^2-508) \\ \Leftrightarrow -10x^2-4=-2x^2+508 \\
\Leftrightarrow -10x^2+2x^2=508+4 \\
\Leftrightarrow -8x^2 = 512 \\
\Leftrightarrow x^2 = \frac{512}{-8} < 0 \\
V = \varnothing \\ -----------------\)
- \(-x^2-64=0 \\
\Leftrightarrow -x^2 = 64 \\
\Leftrightarrow x^2 = \frac{64}{-1} < 0 \\
V = \varnothing \\ -----------------\)
- \(-3(4x^2-3)=-(14x^2-107) \\ \Leftrightarrow -12x^2+9=-14x^2+107 \\
\Leftrightarrow -12x^2+14x^2=107-9 \\
\Leftrightarrow 2x^2 = 98 \\
\Leftrightarrow x^2 = \frac{98}{2}=49 \\
\Leftrightarrow x = 7 \vee x = -7 \\
V = \Big\{-7, 7 \Big\} \\ -----------------\)
- \(7x^2+63=0 \\
\Leftrightarrow 7x^2 = -63 \\
\Leftrightarrow x^2 = \frac{-63}{7} < 0 \\
V = \varnothing \\ -----------------\)
- \(x^2+56=2x^2+7 \\ \Leftrightarrow x^2-2x^2=7-56 \\
\Leftrightarrow -x^2 = -49 \\
\Leftrightarrow x^2 = \frac{-49}{-1}=49 \\
\Leftrightarrow x = 7 \vee x = -7 \\
V = \Big\{-7, 7 \Big\} \\ -----------------\)
- \(x^2+9=0 \\
\Leftrightarrow x^2 = -9 \\
\Leftrightarrow x^2 = \frac{-9}{1} < 0 \\
V = \varnothing \\ -----------------\)
- \(4(7x^2+3)=-(-31x^2+15) \\ \Leftrightarrow 28x^2+12=31x^2-15 \\
\Leftrightarrow 28x^2-31x^2=-15-12 \\
\Leftrightarrow -3x^2 = -27 \\
\Leftrightarrow x^2 = \frac{-27}{-3}=9 \\
\Leftrightarrow x = 3 \vee x = -3 \\
V = \Big\{-3, 3 \Big\} \\ -----------------\)
- \(5x^2-1125=0 \\
\Leftrightarrow 5x^2 = 1125 \\
\Leftrightarrow x^2 = \frac{1125}{5}=225 \\
\Leftrightarrow x = 15 \vee x = -15 \\
V = \Big\{-15, 15 \Big\} \\ -----------------\)
- \(-3x^2+243=0 \\
\Leftrightarrow -3x^2 = -243 \\
\Leftrightarrow x^2 = \frac{-243}{-3}=81 \\
\Leftrightarrow x = 9 \vee x = -9 \\
V = \Big\{-9, 9 \Big\} \\ -----------------\)
- \(6x^2-32=2x^2+4 \\ \Leftrightarrow 6x^2-2x^2=4+32 \\
\Leftrightarrow 4x^2 = 36 \\
\Leftrightarrow x^2 = \frac{36}{4}=9 \\
\Leftrightarrow x = 3 \vee x = -3 \\
V = \Big\{-3, 3 \Big\} \\ -----------------\)