Los de vierkantsvergelijking op zonder de discriminant te gebruiken
- \(4(-4x^2+4)=-(10x^2-400)\)
- \(-4(5x^2-2)=-(13x^2-855)\)
- \(3x^2+48=0\)
- \(-2(-9x^2-5)=-(-26x^2-2)\)
- \(-5(-9x^2+9)=-(-47x^2-27)\)
- \(x^2+225=0\)
- \(8x^2+0=0\)
- \(-x^2-908=3x^2-8\)
- \(x^2-169=0\)
- \(4x^2-1=3x^2+3\)
- \(-11x^2+12=-9x^2+4\)
- \(-3(3x^2-7)=-(3x^2-15)\)
Los de vierkantsvergelijking op zonder de discriminant te gebruiken
Verbetersleutel
- \(4(-4x^2+4)=-(10x^2-400) \\ \Leftrightarrow -16x^2+16=-10x^2+400 \\
\Leftrightarrow -16x^2+10x^2=400-16 \\
\Leftrightarrow -6x^2 = 384 \\
\Leftrightarrow x^2 = \frac{384}{-6} < 0 \\
V = \varnothing \\ -----------------\)
- \(-4(5x^2-2)=-(13x^2-855) \\ \Leftrightarrow -20x^2+8=-13x^2+855 \\
\Leftrightarrow -20x^2+13x^2=855-8 \\
\Leftrightarrow -7x^2 = 847 \\
\Leftrightarrow x^2 = \frac{847}{-7} < 0 \\
V = \varnothing \\ -----------------\)
- \(3x^2+48=0 \\
\Leftrightarrow 3x^2 = -48 \\
\Leftrightarrow x^2 = \frac{-48}{3} < 0 \\
V = \varnothing \\ -----------------\)
- \(-2(-9x^2-5)=-(-26x^2-2) \\ \Leftrightarrow 18x^2+10=26x^2+2 \\
\Leftrightarrow 18x^2-26x^2=2-10 \\
\Leftrightarrow -8x^2 = -8 \\
\Leftrightarrow x^2 = \frac{-8}{-8}=1 \\
\Leftrightarrow x = 1 \vee x = -1 \\
V = \Big\{-1, 1 \Big\} \\ -----------------\)
- \(-5(-9x^2+9)=-(-47x^2-27) \\ \Leftrightarrow 45x^2-45=47x^2+27 \\
\Leftrightarrow 45x^2-47x^2=27+45 \\
\Leftrightarrow -2x^2 = 72 \\
\Leftrightarrow x^2 = \frac{72}{-2} < 0 \\
V = \varnothing \\ -----------------\)
- \(x^2+225=0 \\
\Leftrightarrow x^2 = -225 \\
\Leftrightarrow x^2 = \frac{-225}{1} < 0 \\
V = \varnothing \\ -----------------\)
- \(8x^2+0=0 \\
\Leftrightarrow 8x^2 = 0 \\
\Leftrightarrow x^2 = \frac{0}{8}\\
\Leftrightarrow x = 0 \\
V = \Big\{ 0 \Big\} \\ -----------------\)
- \(-x^2-908=3x^2-8 \\ \Leftrightarrow -x^2-3x^2=-8+908 \\
\Leftrightarrow -4x^2 = 900 \\
\Leftrightarrow x^2 = \frac{900}{-4} < 0 \\
V = \varnothing \\ -----------------\)
- \(x^2-169=0 \\
\Leftrightarrow x^2 = 169 \\
\Leftrightarrow x^2 = \frac{169}{1}=169 \\
\Leftrightarrow x = 13 \vee x = -13 \\
V = \Big\{-13, 13 \Big\} \\ -----------------\)
- \(4x^2-1=3x^2+3 \\ \Leftrightarrow 4x^2-3x^2=3+1 \\
\Leftrightarrow x^2 = 4 \\
\Leftrightarrow x^2 = \frac{4}{1}=4 \\
\Leftrightarrow x = 2 \vee x = -2 \\
V = \Big\{-2, 2 \Big\} \\ -----------------\)
- \(-11x^2+12=-9x^2+4 \\ \Leftrightarrow -11x^2+9x^2=4-12 \\
\Leftrightarrow -2x^2 = -8 \\
\Leftrightarrow x^2 = \frac{-8}{-2}=4 \\
\Leftrightarrow x = 2 \vee x = -2 \\
V = \Big\{-2, 2 \Big\} \\ -----------------\)
- \(-3(3x^2-7)=-(3x^2-15) \\ \Leftrightarrow -9x^2+21=-3x^2+15 \\
\Leftrightarrow -9x^2+3x^2=15-21 \\
\Leftrightarrow -6x^2 = -6 \\
\Leftrightarrow x^2 = \frac{-6}{-6}=1 \\
\Leftrightarrow x = 1 \vee x = -1 \\
V = \Big\{-1, 1 \Big\} \\ -----------------\)