Onvolledige VKV (b=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(-11x^2-162=-10x^2+7\)
2. \(-5x^2+320=0\)
3. \(-5x^2+406=-9x^2+6\)
4. \(2(3x^2-2)=-(-5x^2+20)\)
5. \(-6x^2-486=0\)
6. \(-4(10x^2-9)=-(37x^2-36)\)
7. \(-5(-7x^2+8)=-(-40x^2-140)\)
8. \(-5(6x^2+8)=-(38x^2+1840)\)
9. \(4(3x^2-6)=-(-20x^2+312)\)
10. \(-3(4x^2-4)=-(20x^2+188)\)
11. \(-4(-10x^2-4)=-(-39x^2-160)\)
12. \(-4(-4x^2-4)=-(-11x^2-736)\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(-11x^2-162=-10x^2+7 \\ \Leftrightarrow -11x^2+10x^2=7+162 \\ \Leftrightarrow -x^2 = 169 \\ \Leftrightarrow x^2 = \frac{169}{-1} < 0 \\ V = \varnothing \\ -----------------\)
2. \(-5x^2+320=0 \\ \Leftrightarrow -5x^2 = -320 \\ \Leftrightarrow x^2 = \frac{-320}{-5}=64 \\ \Leftrightarrow x = 8 \vee x = -8 \\ V = \Big\{-8, 8 \Big\} \\ -----------------\)
3. \(-5x^2+406=-9x^2+6 \\ \Leftrightarrow -5x^2+9x^2=6-406 \\ \Leftrightarrow 4x^2 = -400 \\ \Leftrightarrow x^2 = \frac{-400}{4} < 0 \\ V = \varnothing \\ -----------------\)
4. \(2(3x^2-2)=-(-5x^2+20) \\ \Leftrightarrow 6x^2-4=5x^2-20 \\ \Leftrightarrow 6x^2-5x^2=-20+4 \\ \Leftrightarrow x^2 = -16 \\ \Leftrightarrow x^2 = \frac{-16}{1} < 0 \\ V = \varnothing \\ -----------------\)
5. \(-6x^2-486=0 \\ \Leftrightarrow -6x^2 = 486 \\ \Leftrightarrow x^2 = \frac{486}{-6} < 0 \\ V = \varnothing \\ -----------------\)
6. \(-4(10x^2-9)=-(37x^2-36) \\ \Leftrightarrow -40x^2+36=-37x^2+36 \\ \Leftrightarrow -40x^2+37x^2=36-36 \\ \Leftrightarrow -3x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{-3}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
7. \(-5(-7x^2+8)=-(-40x^2-140) \\ \Leftrightarrow 35x^2-40=40x^2+140 \\ \Leftrightarrow 35x^2-40x^2=140+40 \\ \Leftrightarrow -5x^2 = 180 \\ \Leftrightarrow x^2 = \frac{180}{-5} < 0 \\ V = \varnothing \\ -----------------\)
8. \(-5(6x^2+8)=-(38x^2+1840) \\ \Leftrightarrow -30x^2-40=-38x^2-1840 \\ \Leftrightarrow -30x^2+38x^2=-1840+40 \\ \Leftrightarrow 8x^2 = -1800 \\ \Leftrightarrow x^2 = \frac{-1800}{8} < 0 \\ V = \varnothing \\ -----------------\)
9. \(4(3x^2-6)=-(-20x^2+312) \\ \Leftrightarrow 12x^2-24=20x^2-312 \\ \Leftrightarrow 12x^2-20x^2=-312+24 \\ \Leftrightarrow -8x^2 = -288 \\ \Leftrightarrow x^2 = \frac{-288}{-8}=36 \\ \Leftrightarrow x = 6 \vee x = -6 \\ V = \Big\{-6, 6 \Big\} \\ -----------------\)
10. \(-3(4x^2-4)=-(20x^2+188) \\ \Leftrightarrow -12x^2+12=-20x^2-188 \\ \Leftrightarrow -12x^2+20x^2=-188-12 \\ \Leftrightarrow 8x^2 = -200 \\ \Leftrightarrow x^2 = \frac{-200}{8} < 0 \\ V = \varnothing \\ -----------------\)
11. \(-4(-10x^2-4)=-(-39x^2-160) \\ \Leftrightarrow 40x^2+16=39x^2+160 \\ \Leftrightarrow 40x^2-39x^2=160-16 \\ \Leftrightarrow x^2 = 144 \\ \Leftrightarrow x^2 = \frac{144}{1}=144 \\ \Leftrightarrow x = 12 \vee x = -12 \\ V = \Big\{-12, 12 \Big\} \\ -----------------\)
12. \(-4(-4x^2-4)=-(-11x^2-736) \\ \Leftrightarrow 16x^2+16=11x^2+736 \\ \Leftrightarrow 16x^2-11x^2=736-16 \\ \Leftrightarrow 5x^2 = 720 \\ \Leftrightarrow x^2 = \frac{720}{5}=144 \\ \Leftrightarrow x = 12 \vee x = -12 \\ V = \Big\{-12, 12 \Big\} \\ -----------------\)