Los de vierkantsvergelijking op zonder de discriminant te gebruiken
- \(-3x^2+285=3x^2-9\)
- \(-x^2+121=0\)
- \(7x^2-1183=0\)
- \(-x^2+169=0\)
- \(-11x^2+28=-9x^2-4\)
- \(-x^2-81=0\)
- \(-4(-3x^2+4)=-(-19x^2+1199)\)
- \(x^2-144=0\)
- \(12x^2-65=5x^2-2\)
- \(3(6x^2-2)=-(-13x^2+186)\)
- \(-3x^2-108=0\)
- \(3(-7x^2+8)=-(26x^2-69)\)
Los de vierkantsvergelijking op zonder de discriminant te gebruiken
Verbetersleutel
- \(-3x^2+285=3x^2-9 \\ \Leftrightarrow -3x^2-3x^2=-9-285 \\
\Leftrightarrow -6x^2 = -294 \\
\Leftrightarrow x^2 = \frac{-294}{-6}=49 \\
\Leftrightarrow x = 7 \vee x = -7 \\
V = \Big\{-7, 7 \Big\} \\ -----------------\)
- \(-x^2+121=0 \\
\Leftrightarrow -x^2 = -121 \\
\Leftrightarrow x^2 = \frac{-121}{-1}=121 \\
\Leftrightarrow x = 11 \vee x = -11 \\
V = \Big\{-11, 11 \Big\} \\ -----------------\)
- \(7x^2-1183=0 \\
\Leftrightarrow 7x^2 = 1183 \\
\Leftrightarrow x^2 = \frac{1183}{7}=169 \\
\Leftrightarrow x = 13 \vee x = -13 \\
V = \Big\{-13, 13 \Big\} \\ -----------------\)
- \(-x^2+169=0 \\
\Leftrightarrow -x^2 = -169 \\
\Leftrightarrow x^2 = \frac{-169}{-1}=169 \\
\Leftrightarrow x = 13 \vee x = -13 \\
V = \Big\{-13, 13 \Big\} \\ -----------------\)
- \(-11x^2+28=-9x^2-4 \\ \Leftrightarrow -11x^2+9x^2=-4-28 \\
\Leftrightarrow -2x^2 = -32 \\
\Leftrightarrow x^2 = \frac{-32}{-2}=16 \\
\Leftrightarrow x = 4 \vee x = -4 \\
V = \Big\{-4, 4 \Big\} \\ -----------------\)
- \(-x^2-81=0 \\
\Leftrightarrow -x^2 = 81 \\
\Leftrightarrow x^2 = \frac{81}{-1} < 0 \\
V = \varnothing \\ -----------------\)
- \(-4(-3x^2+4)=-(-19x^2+1199) \\ \Leftrightarrow 12x^2-16=19x^2-1199 \\
\Leftrightarrow 12x^2-19x^2=-1199+16 \\
\Leftrightarrow -7x^2 = -1183 \\
\Leftrightarrow x^2 = \frac{-1183}{-7}=169 \\
\Leftrightarrow x = 13 \vee x = -13 \\
V = \Big\{-13, 13 \Big\} \\ -----------------\)
- \(x^2-144=0 \\
\Leftrightarrow x^2 = 144 \\
\Leftrightarrow x^2 = \frac{144}{1}=144 \\
\Leftrightarrow x = 12 \vee x = -12 \\
V = \Big\{-12, 12 \Big\} \\ -----------------\)
- \(12x^2-65=5x^2-2 \\ \Leftrightarrow 12x^2-5x^2=-2+65 \\
\Leftrightarrow 7x^2 = 63 \\
\Leftrightarrow x^2 = \frac{63}{7}=9 \\
\Leftrightarrow x = 3 \vee x = -3 \\
V = \Big\{-3, 3 \Big\} \\ -----------------\)
- \(3(6x^2-2)=-(-13x^2+186) \\ \Leftrightarrow 18x^2-6=13x^2-186 \\
\Leftrightarrow 18x^2-13x^2=-186+6 \\
\Leftrightarrow 5x^2 = -180 \\
\Leftrightarrow x^2 = \frac{-180}{5} < 0 \\
V = \varnothing \\ -----------------\)
- \(-3x^2-108=0 \\
\Leftrightarrow -3x^2 = 108 \\
\Leftrightarrow x^2 = \frac{108}{-3} < 0 \\
V = \varnothing \\ -----------------\)
- \(3(-7x^2+8)=-(26x^2-69) \\ \Leftrightarrow -21x^2+24=-26x^2+69 \\
\Leftrightarrow -21x^2+26x^2=69-24 \\
\Leftrightarrow 5x^2 = 45 \\
\Leftrightarrow x^2 = \frac{45}{5}=9 \\
\Leftrightarrow x = 3 \vee x = -3 \\
V = \Big\{-3, 3 \Big\} \\ -----------------\)