Los de vierkantsvergelijking op zonder de discriminant te gebruiken
- \(7x^2-489=3x^2-5\)
- \(-x^2+225=0\)
- \(4(-3x^2-2)=-(19x^2-1567)\)
- \(-4(-4x^2+4)=-(-11x^2-4)\)
- \(6x^2-24=0\)
- \(2(10x^2-8)=-(-14x^2+40)\)
- \(17x^2-9=10x^2-9\)
- \(5(-3x^2-8)=-(14x^2+140)\)
- \(x^2-4=0\)
- \(7x^2-1008=0\)
- \(5(4x^2-2)=-(-23x^2+10)\)
- \(-5x^2+245=0\)
Los de vierkantsvergelijking op zonder de discriminant te gebruiken
Verbetersleutel
- \(7x^2-489=3x^2-5 \\ \Leftrightarrow 7x^2-3x^2=-5+489 \\
\Leftrightarrow 4x^2 = 484 \\
\Leftrightarrow x^2 = \frac{484}{4}=121 \\
\Leftrightarrow x = 11 \vee x = -11 \\
V = \Big\{-11, 11 \Big\} \\ -----------------\)
- \(-x^2+225=0 \\
\Leftrightarrow -x^2 = -225 \\
\Leftrightarrow x^2 = \frac{-225}{-1}=225 \\
\Leftrightarrow x = 15 \vee x = -15 \\
V = \Big\{-15, 15 \Big\} \\ -----------------\)
- \(4(-3x^2-2)=-(19x^2-1567) \\ \Leftrightarrow -12x^2-8=-19x^2+1567 \\
\Leftrightarrow -12x^2+19x^2=1567+8 \\
\Leftrightarrow 7x^2 = 1575 \\
\Leftrightarrow x^2 = \frac{1575}{7}=225 \\
\Leftrightarrow x = 15 \vee x = -15 \\
V = \Big\{-15, 15 \Big\} \\ -----------------\)
- \(-4(-4x^2+4)=-(-11x^2-4) \\ \Leftrightarrow 16x^2-16=11x^2+4 \\
\Leftrightarrow 16x^2-11x^2=4+16 \\
\Leftrightarrow 5x^2 = 20 \\
\Leftrightarrow x^2 = \frac{20}{5}=4 \\
\Leftrightarrow x = 2 \vee x = -2 \\
V = \Big\{-2, 2 \Big\} \\ -----------------\)
- \(6x^2-24=0 \\
\Leftrightarrow 6x^2 = 24 \\
\Leftrightarrow x^2 = \frac{24}{6}=4 \\
\Leftrightarrow x = 2 \vee x = -2 \\
V = \Big\{-2, 2 \Big\} \\ -----------------\)
- \(2(10x^2-8)=-(-14x^2+40) \\ \Leftrightarrow 20x^2-16=14x^2-40 \\
\Leftrightarrow 20x^2-14x^2=-40+16 \\
\Leftrightarrow 6x^2 = -24 \\
\Leftrightarrow x^2 = \frac{-24}{6} < 0 \\
V = \varnothing \\ -----------------\)
- \(17x^2-9=10x^2-9 \\ \Leftrightarrow 17x^2-10x^2=-9+9 \\
\Leftrightarrow 7x^2 = 0 \\
\Leftrightarrow x^2 = \frac{0}{7}\\
\Leftrightarrow x = 0 \\
V = \Big\{ 0 \Big\} \\ -----------------\)
- \(5(-3x^2-8)=-(14x^2+140) \\ \Leftrightarrow -15x^2-40=-14x^2-140 \\
\Leftrightarrow -15x^2+14x^2=-140+40 \\
\Leftrightarrow -x^2 = -100 \\
\Leftrightarrow x^2 = \frac{-100}{-1}=100 \\
\Leftrightarrow x = 10 \vee x = -10 \\
V = \Big\{-10, 10 \Big\} \\ -----------------\)
- \(x^2-4=0 \\
\Leftrightarrow x^2 = 4 \\
\Leftrightarrow x^2 = \frac{4}{1}=4 \\
\Leftrightarrow x = 2 \vee x = -2 \\
V = \Big\{-2, 2 \Big\} \\ -----------------\)
- \(7x^2-1008=0 \\
\Leftrightarrow 7x^2 = 1008 \\
\Leftrightarrow x^2 = \frac{1008}{7}=144 \\
\Leftrightarrow x = 12 \vee x = -12 \\
V = \Big\{-12, 12 \Big\} \\ -----------------\)
- \(5(4x^2-2)=-(-23x^2+10) \\ \Leftrightarrow 20x^2-10=23x^2-10 \\
\Leftrightarrow 20x^2-23x^2=-10+10 \\
\Leftrightarrow -3x^2 = 0 \\
\Leftrightarrow x^2 = \frac{0}{-3}\\
\Leftrightarrow x = 0 \\
V = \Big\{ 0 \Big\} \\ -----------------\)
- \(-5x^2+245=0 \\
\Leftrightarrow -5x^2 = -245 \\
\Leftrightarrow x^2 = \frac{-245}{-5}=49 \\
\Leftrightarrow x = 7 \vee x = -7 \\
V = \Big\{-7, 7 \Big\} \\ -----------------\)