Onvolledige VKV (b=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(5x^2-125=0\)
2. \(3(-6x^2+8)=-(13x^2-524)\)
3. \(x^2+10=6x^2+10\)
4. \(2(-5x^2+6)=-(14x^2+312)\)
5. \(5x^2+671=9x^2-5\)
6. \(8x^2+0=0\)
7. \(3(-3x^2-9)=-(11x^2+269)\)
8. \(-x^2-313=-6x^2+7\)
9. \(17x^2+337=10x^2-6\)
10. \(4(4x^2-6)=-(-14x^2+56)\)
11. \(14x^2+872=8x^2+8\)
12. \(-6x^2-6=-4x^2+2\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(5x^2-125=0 \\ \Leftrightarrow 5x^2 = 125 \\ \Leftrightarrow x^2 = \frac{125}{5}=25 \\ \Leftrightarrow x = 5 \vee x = -5 \\ V = \Big\{-5, 5 \Big\} \\ -----------------\)
2. \(3(-6x^2+8)=-(13x^2-524) \\ \Leftrightarrow -18x^2+24=-13x^2+524 \\ \Leftrightarrow -18x^2+13x^2=524-24 \\ \Leftrightarrow -5x^2 = 500 \\ \Leftrightarrow x^2 = \frac{500}{-5} < 0 \\ V = \varnothing \\ -----------------\)
3. \(x^2+10=6x^2+10 \\ \Leftrightarrow x^2-6x^2=10-10 \\ \Leftrightarrow -5x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{-5}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
4. \(2(-5x^2+6)=-(14x^2+312) \\ \Leftrightarrow -10x^2+12=-14x^2-312 \\ \Leftrightarrow -10x^2+14x^2=-312-12 \\ \Leftrightarrow 4x^2 = -324 \\ \Leftrightarrow x^2 = \frac{-324}{4} < 0 \\ V = \varnothing \\ -----------------\)
5. \(5x^2+671=9x^2-5 \\ \Leftrightarrow 5x^2-9x^2=-5-671 \\ \Leftrightarrow -4x^2 = -676 \\ \Leftrightarrow x^2 = \frac{-676}{-4}=169 \\ \Leftrightarrow x = 13 \vee x = -13 \\ V = \Big\{-13, 13 \Big\} \\ -----------------\)
6. \(8x^2+0=0 \\ \Leftrightarrow 8x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{8}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
7. \(3(-3x^2-9)=-(11x^2+269) \\ \Leftrightarrow -9x^2-27=-11x^2-269 \\ \Leftrightarrow -9x^2+11x^2=-269+27 \\ \Leftrightarrow 2x^2 = -242 \\ \Leftrightarrow x^2 = \frac{-242}{2} < 0 \\ V = \varnothing \\ -----------------\)
8. \(-x^2-313=-6x^2+7 \\ \Leftrightarrow -x^2+6x^2=7+313 \\ \Leftrightarrow 5x^2 = 320 \\ \Leftrightarrow x^2 = \frac{320}{5}=64 \\ \Leftrightarrow x = 8 \vee x = -8 \\ V = \Big\{-8, 8 \Big\} \\ -----------------\)
9. \(17x^2+337=10x^2-6 \\ \Leftrightarrow 17x^2-10x^2=-6-337 \\ \Leftrightarrow 7x^2 = -343 \\ \Leftrightarrow x^2 = \frac{-343}{7} < 0 \\ V = \varnothing \\ -----------------\)
10. \(4(4x^2-6)=-(-14x^2+56) \\ \Leftrightarrow 16x^2-24=14x^2-56 \\ \Leftrightarrow 16x^2-14x^2=-56+24 \\ \Leftrightarrow 2x^2 = -32 \\ \Leftrightarrow x^2 = \frac{-32}{2} < 0 \\ V = \varnothing \\ -----------------\)
11. \(14x^2+872=8x^2+8 \\ \Leftrightarrow 14x^2-8x^2=8-872 \\ \Leftrightarrow 6x^2 = -864 \\ \Leftrightarrow x^2 = \frac{-864}{6} < 0 \\ V = \varnothing \\ -----------------\)
12. \(-6x^2-6=-4x^2+2 \\ \Leftrightarrow -6x^2+4x^2=2+6 \\ \Leftrightarrow -2x^2 = 8 \\ \Leftrightarrow x^2 = \frac{8}{-2} < 0 \\ V = \varnothing \\ -----------------\)