Los de vierkantsvergelijking op zonder de discriminant te gebruiken
- \(-3x^2-588=0\)
- \(-6x^2-864=0\)
- \(-5x^2+45=0\)
- \(x^2+16=0\)
- \(-4x^2-196=0\)
- \(6x^2-150=0\)
- \(-4(-3x^2+2)=-(-13x^2+108)\)
- \(-9x^2-39=-8x^2+10\)
- \(5(-10x^2-3)=-(42x^2-273)\)
- \(-8x^2-512=0\)
- \(6x^2-54=0\)
- \(2(7x^2-7)=-(-8x^2-1336)\)
Los de vierkantsvergelijking op zonder de discriminant te gebruiken
Verbetersleutel
- \(-3x^2-588=0 \\
\Leftrightarrow -3x^2 = 588 \\
\Leftrightarrow x^2 = \frac{588}{-3} < 0 \\
V = \varnothing \\ -----------------\)
- \(-6x^2-864=0 \\
\Leftrightarrow -6x^2 = 864 \\
\Leftrightarrow x^2 = \frac{864}{-6} < 0 \\
V = \varnothing \\ -----------------\)
- \(-5x^2+45=0 \\
\Leftrightarrow -5x^2 = -45 \\
\Leftrightarrow x^2 = \frac{-45}{-5}=9 \\
\Leftrightarrow x = 3 \vee x = -3 \\
V = \Big\{-3, 3 \Big\} \\ -----------------\)
- \(x^2+16=0 \\
\Leftrightarrow x^2 = -16 \\
\Leftrightarrow x^2 = \frac{-16}{1} < 0 \\
V = \varnothing \\ -----------------\)
- \(-4x^2-196=0 \\
\Leftrightarrow -4x^2 = 196 \\
\Leftrightarrow x^2 = \frac{196}{-4} < 0 \\
V = \varnothing \\ -----------------\)
- \(6x^2-150=0 \\
\Leftrightarrow 6x^2 = 150 \\
\Leftrightarrow x^2 = \frac{150}{6}=25 \\
\Leftrightarrow x = 5 \vee x = -5 \\
V = \Big\{-5, 5 \Big\} \\ -----------------\)
- \(-4(-3x^2+2)=-(-13x^2+108) \\ \Leftrightarrow 12x^2-8=13x^2-108 \\
\Leftrightarrow 12x^2-13x^2=-108+8 \\
\Leftrightarrow -x^2 = -100 \\
\Leftrightarrow x^2 = \frac{-100}{-1}=100 \\
\Leftrightarrow x = 10 \vee x = -10 \\
V = \Big\{-10, 10 \Big\} \\ -----------------\)
- \(-9x^2-39=-8x^2+10 \\ \Leftrightarrow -9x^2+8x^2=10+39 \\
\Leftrightarrow -x^2 = 49 \\
\Leftrightarrow x^2 = \frac{49}{-1} < 0 \\
V = \varnothing \\ -----------------\)
- \(5(-10x^2-3)=-(42x^2-273) \\ \Leftrightarrow -50x^2-15=-42x^2+273 \\
\Leftrightarrow -50x^2+42x^2=273+15 \\
\Leftrightarrow -8x^2 = 288 \\
\Leftrightarrow x^2 = \frac{288}{-8} < 0 \\
V = \varnothing \\ -----------------\)
- \(-8x^2-512=0 \\
\Leftrightarrow -8x^2 = 512 \\
\Leftrightarrow x^2 = \frac{512}{-8} < 0 \\
V = \varnothing \\ -----------------\)
- \(6x^2-54=0 \\
\Leftrightarrow 6x^2 = 54 \\
\Leftrightarrow x^2 = \frac{54}{6}=9 \\
\Leftrightarrow x = 3 \vee x = -3 \\
V = \Big\{-3, 3 \Big\} \\ -----------------\)
- \(2(7x^2-7)=-(-8x^2-1336) \\ \Leftrightarrow 14x^2-14=8x^2+1336 \\
\Leftrightarrow 14x^2-8x^2=1336+14 \\
\Leftrightarrow 6x^2 = 1350 \\
\Leftrightarrow x^2 = \frac{1350}{6}=225 \\
\Leftrightarrow x = 15 \vee x = -15 \\
V = \Big\{-15, 15 \Big\} \\ -----------------\)