Los de vierkantsvergelijking op zonder de discriminant te gebruiken
- \(2x^2+304=5x^2+4\)
- \(2(-6x^2+9)=-(7x^2+702)\)
- \(4x^2-16=0\)
- \(x^2+225=0\)
- \(-5(5x^2-7)=-(27x^2+357)\)
- \(2(2x^2+5)=-(2x^2-304)\)
- \(7x^2+448=0\)
- \(-2x^2-89=-8x^2+7\)
- \(-2(-10x^2-2)=-(-26x^2-154)\)
- \(-10x^2+2=-7x^2+2\)
- \(10x^2-220=9x^2+5\)
- \(-5(-7x^2-9)=-(-41x^2+555)\)
Los de vierkantsvergelijking op zonder de discriminant te gebruiken
Verbetersleutel
- \(2x^2+304=5x^2+4 \\ \Leftrightarrow 2x^2-5x^2=4-304 \\
\Leftrightarrow -3x^2 = -300 \\
\Leftrightarrow x^2 = \frac{-300}{-3}=100 \\
\Leftrightarrow x = 10 \vee x = -10 \\
V = \Big\{-10, 10 \Big\} \\ -----------------\)
- \(2(-6x^2+9)=-(7x^2+702) \\ \Leftrightarrow -12x^2+18=-7x^2-702 \\
\Leftrightarrow -12x^2+7x^2=-702-18 \\
\Leftrightarrow -5x^2 = -720 \\
\Leftrightarrow x^2 = \frac{-720}{-5}=144 \\
\Leftrightarrow x = 12 \vee x = -12 \\
V = \Big\{-12, 12 \Big\} \\ -----------------\)
- \(4x^2-16=0 \\
\Leftrightarrow 4x^2 = 16 \\
\Leftrightarrow x^2 = \frac{16}{4}=4 \\
\Leftrightarrow x = 2 \vee x = -2 \\
V = \Big\{-2, 2 \Big\} \\ -----------------\)
- \(x^2+225=0 \\
\Leftrightarrow x^2 = -225 \\
\Leftrightarrow x^2 = \frac{-225}{1} < 0 \\
V = \varnothing \\ -----------------\)
- \(-5(5x^2-7)=-(27x^2+357) \\ \Leftrightarrow -25x^2+35=-27x^2-357 \\
\Leftrightarrow -25x^2+27x^2=-357-35 \\
\Leftrightarrow 2x^2 = -392 \\
\Leftrightarrow x^2 = \frac{-392}{2} < 0 \\
V = \varnothing \\ -----------------\)
- \(2(2x^2+5)=-(2x^2-304) \\ \Leftrightarrow 4x^2+10=-2x^2+304 \\
\Leftrightarrow 4x^2+2x^2=304-10 \\
\Leftrightarrow 6x^2 = 294 \\
\Leftrightarrow x^2 = \frac{294}{6}=49 \\
\Leftrightarrow x = 7 \vee x = -7 \\
V = \Big\{-7, 7 \Big\} \\ -----------------\)
- \(7x^2+448=0 \\
\Leftrightarrow 7x^2 = -448 \\
\Leftrightarrow x^2 = \frac{-448}{7} < 0 \\
V = \varnothing \\ -----------------\)
- \(-2x^2-89=-8x^2+7 \\ \Leftrightarrow -2x^2+8x^2=7+89 \\
\Leftrightarrow 6x^2 = 96 \\
\Leftrightarrow x^2 = \frac{96}{6}=16 \\
\Leftrightarrow x = 4 \vee x = -4 \\
V = \Big\{-4, 4 \Big\} \\ -----------------\)
- \(-2(-10x^2-2)=-(-26x^2-154) \\ \Leftrightarrow 20x^2+4=26x^2+154 \\
\Leftrightarrow 20x^2-26x^2=154-4 \\
\Leftrightarrow -6x^2 = 150 \\
\Leftrightarrow x^2 = \frac{150}{-6} < 0 \\
V = \varnothing \\ -----------------\)
- \(-10x^2+2=-7x^2+2 \\ \Leftrightarrow -10x^2+7x^2=2-2 \\
\Leftrightarrow -3x^2 = 0 \\
\Leftrightarrow x^2 = \frac{0}{-3}\\
\Leftrightarrow x = 0 \\
V = \Big\{ 0 \Big\} \\ -----------------\)
- \(10x^2-220=9x^2+5 \\ \Leftrightarrow 10x^2-9x^2=5+220 \\
\Leftrightarrow x^2 = 225 \\
\Leftrightarrow x^2 = \frac{225}{1}=225 \\
\Leftrightarrow x = 15 \vee x = -15 \\
V = \Big\{-15, 15 \Big\} \\ -----------------\)
- \(-5(-7x^2-9)=-(-41x^2+555) \\ \Leftrightarrow 35x^2+45=41x^2-555 \\
\Leftrightarrow 35x^2-41x^2=-555-45 \\
\Leftrightarrow -6x^2 = -600 \\
\Leftrightarrow x^2 = \frac{-600}{-6}=100 \\
\Leftrightarrow x = 10 \vee x = -10 \\
V = \Big\{-10, 10 \Big\} \\ -----------------\)