Los de vierkantsvergelijking op zonder de discriminant te gebruiken
- \(4x^2+484=0\)
- \(-3x^2+675=0\)
- \(4(-5x^2-2)=-(18x^2+136)\)
- \(-6x^2+1176=0\)
- \(-4(4x^2-8)=-(21x^2+373)\)
- \(2(9x^2-7)=-(-12x^2-280)\)
- \(-5x^2-726=-10x^2-6\)
- \(4x^2-115=3x^2+6\)
- \(-4x^2+1572=4x^2+4\)
- \(x^2-315=-3x^2+9\)
- \(-8x^2-288=0\)
- \(-5x^2-980=0\)
Los de vierkantsvergelijking op zonder de discriminant te gebruiken
Verbetersleutel
- \(4x^2+484=0 \\
\Leftrightarrow 4x^2 = -484 \\
\Leftrightarrow x^2 = \frac{-484}{4} < 0 \\
V = \varnothing \\ -----------------\)
- \(-3x^2+675=0 \\
\Leftrightarrow -3x^2 = -675 \\
\Leftrightarrow x^2 = \frac{-675}{-3}=225 \\
\Leftrightarrow x = 15 \vee x = -15 \\
V = \Big\{-15, 15 \Big\} \\ -----------------\)
- \(4(-5x^2-2)=-(18x^2+136) \\ \Leftrightarrow -20x^2-8=-18x^2-136 \\
\Leftrightarrow -20x^2+18x^2=-136+8 \\
\Leftrightarrow -2x^2 = -128 \\
\Leftrightarrow x^2 = \frac{-128}{-2}=64 \\
\Leftrightarrow x = 8 \vee x = -8 \\
V = \Big\{-8, 8 \Big\} \\ -----------------\)
- \(-6x^2+1176=0 \\
\Leftrightarrow -6x^2 = -1176 \\
\Leftrightarrow x^2 = \frac{-1176}{-6}=196 \\
\Leftrightarrow x = 14 \vee x = -14 \\
V = \Big\{-14, 14 \Big\} \\ -----------------\)
- \(-4(4x^2-8)=-(21x^2+373) \\ \Leftrightarrow -16x^2+32=-21x^2-373 \\
\Leftrightarrow -16x^2+21x^2=-373-32 \\
\Leftrightarrow 5x^2 = -405 \\
\Leftrightarrow x^2 = \frac{-405}{5} < 0 \\
V = \varnothing \\ -----------------\)
- \(2(9x^2-7)=-(-12x^2-280) \\ \Leftrightarrow 18x^2-14=12x^2+280 \\
\Leftrightarrow 18x^2-12x^2=280+14 \\
\Leftrightarrow 6x^2 = 294 \\
\Leftrightarrow x^2 = \frac{294}{6}=49 \\
\Leftrightarrow x = 7 \vee x = -7 \\
V = \Big\{-7, 7 \Big\} \\ -----------------\)
- \(-5x^2-726=-10x^2-6 \\ \Leftrightarrow -5x^2+10x^2=-6+726 \\
\Leftrightarrow 5x^2 = 720 \\
\Leftrightarrow x^2 = \frac{720}{5}=144 \\
\Leftrightarrow x = 12 \vee x = -12 \\
V = \Big\{-12, 12 \Big\} \\ -----------------\)
- \(4x^2-115=3x^2+6 \\ \Leftrightarrow 4x^2-3x^2=6+115 \\
\Leftrightarrow x^2 = 121 \\
\Leftrightarrow x^2 = \frac{121}{1}=121 \\
\Leftrightarrow x = 11 \vee x = -11 \\
V = \Big\{-11, 11 \Big\} \\ -----------------\)
- \(-4x^2+1572=4x^2+4 \\ \Leftrightarrow -4x^2-4x^2=4-1572 \\
\Leftrightarrow -8x^2 = -1568 \\
\Leftrightarrow x^2 = \frac{-1568}{-8}=196 \\
\Leftrightarrow x = 14 \vee x = -14 \\
V = \Big\{-14, 14 \Big\} \\ -----------------\)
- \(x^2-315=-3x^2+9 \\ \Leftrightarrow x^2+3x^2=9+315 \\
\Leftrightarrow 4x^2 = 324 \\
\Leftrightarrow x^2 = \frac{324}{4}=81 \\
\Leftrightarrow x = 9 \vee x = -9 \\
V = \Big\{-9, 9 \Big\} \\ -----------------\)
- \(-8x^2-288=0 \\
\Leftrightarrow -8x^2 = 288 \\
\Leftrightarrow x^2 = \frac{288}{-8} < 0 \\
V = \varnothing \\ -----------------\)
- \(-5x^2-980=0 \\
\Leftrightarrow -5x^2 = 980 \\
\Leftrightarrow x^2 = \frac{980}{-5} < 0 \\
V = \varnothing \\ -----------------\)