Los de vierkantsvergelijking op zonder de discriminant te gebruiken
- \(-2x^2+319=-6x^2-5\)
- \(-2x^2-92=-3x^2+8\)
- \(-x^2+36=0\)
- \(-5x^2-1570=3x^2-2\)
- \(6x^2-1014=0\)
- \(-5(-9x^2-9)=-(-50x^2-170)\)
- \(-4(-7x^2-5)=-(-30x^2+78)\)
- \(15x^2-49=9x^2+5\)
- \(-5(-8x^2+8)=-(-39x^2-41)\)
- \(-2(-2x^2+7)=-(-x^2-493)\)
- \(-6x^2-150=0\)
- \(2(-9x^2-3)=-(13x^2+11)\)
Los de vierkantsvergelijking op zonder de discriminant te gebruiken
Verbetersleutel
- \(-2x^2+319=-6x^2-5 \\ \Leftrightarrow -2x^2+6x^2=-5-319 \\
\Leftrightarrow 4x^2 = -324 \\
\Leftrightarrow x^2 = \frac{-324}{4} < 0 \\
V = \varnothing \\ -----------------\)
- \(-2x^2-92=-3x^2+8 \\ \Leftrightarrow -2x^2+3x^2=8+92 \\
\Leftrightarrow x^2 = 100 \\
\Leftrightarrow x^2 = \frac{100}{1}=100 \\
\Leftrightarrow x = 10 \vee x = -10 \\
V = \Big\{-10, 10 \Big\} \\ -----------------\)
- \(-x^2+36=0 \\
\Leftrightarrow -x^2 = -36 \\
\Leftrightarrow x^2 = \frac{-36}{-1}=36 \\
\Leftrightarrow x = 6 \vee x = -6 \\
V = \Big\{-6, 6 \Big\} \\ -----------------\)
- \(-5x^2-1570=3x^2-2 \\ \Leftrightarrow -5x^2-3x^2=-2+1570 \\
\Leftrightarrow -8x^2 = 1568 \\
\Leftrightarrow x^2 = \frac{1568}{-8} < 0 \\
V = \varnothing \\ -----------------\)
- \(6x^2-1014=0 \\
\Leftrightarrow 6x^2 = 1014 \\
\Leftrightarrow x^2 = \frac{1014}{6}=169 \\
\Leftrightarrow x = 13 \vee x = -13 \\
V = \Big\{-13, 13 \Big\} \\ -----------------\)
- \(-5(-9x^2-9)=-(-50x^2-170) \\ \Leftrightarrow 45x^2+45=50x^2+170 \\
\Leftrightarrow 45x^2-50x^2=170-45 \\
\Leftrightarrow -5x^2 = 125 \\
\Leftrightarrow x^2 = \frac{125}{-5} < 0 \\
V = \varnothing \\ -----------------\)
- \(-4(-7x^2-5)=-(-30x^2+78) \\ \Leftrightarrow 28x^2+20=30x^2-78 \\
\Leftrightarrow 28x^2-30x^2=-78-20 \\
\Leftrightarrow -2x^2 = -98 \\
\Leftrightarrow x^2 = \frac{-98}{-2}=49 \\
\Leftrightarrow x = 7 \vee x = -7 \\
V = \Big\{-7, 7 \Big\} \\ -----------------\)
- \(15x^2-49=9x^2+5 \\ \Leftrightarrow 15x^2-9x^2=5+49 \\
\Leftrightarrow 6x^2 = 54 \\
\Leftrightarrow x^2 = \frac{54}{6}=9 \\
\Leftrightarrow x = 3 \vee x = -3 \\
V = \Big\{-3, 3 \Big\} \\ -----------------\)
- \(-5(-8x^2+8)=-(-39x^2-41) \\ \Leftrightarrow 40x^2-40=39x^2+41 \\
\Leftrightarrow 40x^2-39x^2=41+40 \\
\Leftrightarrow x^2 = 81 \\
\Leftrightarrow x^2 = \frac{81}{1}=81 \\
\Leftrightarrow x = 9 \vee x = -9 \\
V = \Big\{-9, 9 \Big\} \\ -----------------\)
- \(-2(-2x^2+7)=-(-x^2-493) \\ \Leftrightarrow 4x^2-14=x^2+493 \\
\Leftrightarrow 4x^2-x^2=493+14 \\
\Leftrightarrow 3x^2 = 507 \\
\Leftrightarrow x^2 = \frac{507}{3}=169 \\
\Leftrightarrow x = 13 \vee x = -13 \\
V = \Big\{-13, 13 \Big\} \\ -----------------\)
- \(-6x^2-150=0 \\
\Leftrightarrow -6x^2 = 150 \\
\Leftrightarrow x^2 = \frac{150}{-6} < 0 \\
V = \varnothing \\ -----------------\)
- \(2(-9x^2-3)=-(13x^2+11) \\ \Leftrightarrow -18x^2-6=-13x^2-11 \\
\Leftrightarrow -18x^2+13x^2=-11+6 \\
\Leftrightarrow -5x^2 = -5 \\
\Leftrightarrow x^2 = \frac{-5}{-5}=1 \\
\Leftrightarrow x = 1 \vee x = -1 \\
V = \Big\{-1, 1 \Big\} \\ -----------------\)