Los de vierkantsvergelijking op zonder de discriminant te gebruiken
- \(-4(3x^2-8)=-(18x^2-416)\)
- \(-7x^2+252=0\)
- \(-3(3x^2+3)=-(7x^2+59)\)
- \(-3(10x^2-4)=-(32x^2+6)\)
- \(2x^2-1173=8x^2+3\)
- \(x^2+16=0\)
- \(12x^2-11=10x^2-3\)
- \(-12x^2+1576=-4x^2+8\)
- \(3(-5x^2-9)=-(19x^2+11)\)
- \(-2x^2+0=0\)
- \(-3(5x^2+3)=-(19x^2-247)\)
- \(-7x^2+0=0\)
Los de vierkantsvergelijking op zonder de discriminant te gebruiken
Verbetersleutel
- \(-4(3x^2-8)=-(18x^2-416) \\ \Leftrightarrow -12x^2+32=-18x^2+416 \\
\Leftrightarrow -12x^2+18x^2=416-32 \\
\Leftrightarrow 6x^2 = 384 \\
\Leftrightarrow x^2 = \frac{384}{6}=64 \\
\Leftrightarrow x = 8 \vee x = -8 \\
V = \Big\{-8, 8 \Big\} \\ -----------------\)
- \(-7x^2+252=0 \\
\Leftrightarrow -7x^2 = -252 \\
\Leftrightarrow x^2 = \frac{-252}{-7}=36 \\
\Leftrightarrow x = 6 \vee x = -6 \\
V = \Big\{-6, 6 \Big\} \\ -----------------\)
- \(-3(3x^2+3)=-(7x^2+59) \\ \Leftrightarrow -9x^2-9=-7x^2-59 \\
\Leftrightarrow -9x^2+7x^2=-59+9 \\
\Leftrightarrow -2x^2 = -50 \\
\Leftrightarrow x^2 = \frac{-50}{-2}=25 \\
\Leftrightarrow x = 5 \vee x = -5 \\
V = \Big\{-5, 5 \Big\} \\ -----------------\)
- \(-3(10x^2-4)=-(32x^2+6) \\ \Leftrightarrow -30x^2+12=-32x^2-6 \\
\Leftrightarrow -30x^2+32x^2=-6-12 \\
\Leftrightarrow 2x^2 = -18 \\
\Leftrightarrow x^2 = \frac{-18}{2} < 0 \\
V = \varnothing \\ -----------------\)
- \(2x^2-1173=8x^2+3 \\ \Leftrightarrow 2x^2-8x^2=3+1173 \\
\Leftrightarrow -6x^2 = 1176 \\
\Leftrightarrow x^2 = \frac{1176}{-6} < 0 \\
V = \varnothing \\ -----------------\)
- \(x^2+16=0 \\
\Leftrightarrow x^2 = -16 \\
\Leftrightarrow x^2 = \frac{-16}{1} < 0 \\
V = \varnothing \\ -----------------\)
- \(12x^2-11=10x^2-3 \\ \Leftrightarrow 12x^2-10x^2=-3+11 \\
\Leftrightarrow 2x^2 = 8 \\
\Leftrightarrow x^2 = \frac{8}{2}=4 \\
\Leftrightarrow x = 2 \vee x = -2 \\
V = \Big\{-2, 2 \Big\} \\ -----------------\)
- \(-12x^2+1576=-4x^2+8 \\ \Leftrightarrow -12x^2+4x^2=8-1576 \\
\Leftrightarrow -8x^2 = -1568 \\
\Leftrightarrow x^2 = \frac{-1568}{-8}=196 \\
\Leftrightarrow x = 14 \vee x = -14 \\
V = \Big\{-14, 14 \Big\} \\ -----------------\)
- \(3(-5x^2-9)=-(19x^2+11) \\ \Leftrightarrow -15x^2-27=-19x^2-11 \\
\Leftrightarrow -15x^2+19x^2=-11+27 \\
\Leftrightarrow 4x^2 = 16 \\
\Leftrightarrow x^2 = \frac{16}{4}=4 \\
\Leftrightarrow x = 2 \vee x = -2 \\
V = \Big\{-2, 2 \Big\} \\ -----------------\)
- \(-2x^2+0=0 \\
\Leftrightarrow -2x^2 = 0 \\
\Leftrightarrow x^2 = \frac{0}{-2}\\
\Leftrightarrow x = 0 \\
V = \Big\{ 0 \Big\} \\ -----------------\)
- \(-3(5x^2+3)=-(19x^2-247) \\ \Leftrightarrow -15x^2-9=-19x^2+247 \\
\Leftrightarrow -15x^2+19x^2=247+9 \\
\Leftrightarrow 4x^2 = 256 \\
\Leftrightarrow x^2 = \frac{256}{4}=64 \\
\Leftrightarrow x = 8 \vee x = -8 \\
V = \Big\{-8, 8 \Big\} \\ -----------------\)
- \(-7x^2+0=0 \\
\Leftrightarrow -7x^2 = 0 \\
\Leftrightarrow x^2 = \frac{0}{-7}\\
\Leftrightarrow x = 0 \\
V = \Big\{ 0 \Big\} \\ -----------------\)