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If the roots of the equation ax^2 + bx +...

If the roots of the equation `ax^2 + bx + c = 0` are in the ratio `2:3`, then prove that `6b^2 = 25ac`

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KALYANI PUBLICATION-ALGEBRIC METHOD OF SOLVING A PAIR OF LINEAR EQUATIONS-EXERCISE
  1. If the roots of the equation ax^2 + bx + c = 0 are in the ratio 2:3, t...

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  2. Solve by the method of elimination: 5x-3y=1, 2x+5y=19

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  3. Solve by the method of elimination: 3x+4y=7, 5x-8y=8

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  4. Solve by the method of elimination: 5x-3y=16, 3x-y=12

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  5. Solve by the method of substitution: 2x+3y=31, 17x-11y=8

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  6. Solve by the method of substitution: ax+by=1, bx+ay=(a+b)^2/(a^2+b^2...

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  7. Solve by the method of substitution: x+y=a+b, ax-by=a^2-b^2

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  8. Solve by the method of cross multiplication: 8x+3y=1, 7x+4y=-6

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  9. Solve by the method of cross multiplication: 2x+y=35, 3x+4y=65

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  10. Solve by the method of cross multiplication: ax+by=a-b, bx-ay=a+b

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  11. Solve by any method: (xy)/(x+y)=6/5, (xy)/(y-x)=6

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  12. Solve by any method: (x+y)/(xy)=1, (x-y)/(xy)=65

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  13. Solve by any method: x+2y=1.3, 3/(2x+5y)=1

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  14. Solve by any method: 31x+43y=117, 43x+31y=105

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  15. Solve by any method: 148x+231y=527, 231x+148y=610

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  16. Solve by any method: ax+by=c, bx+ay=1+c

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  17. Solve by any method: x+5y=36, (x+y)/(x-y)=5/3

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  18. Solve by any method: x-y=0.9, 11/(2(x+y))=1

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  19. Solve by any method: x/a+y/b=a+b, x/a^2+y/b^2=2

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  20. Solve by any method: x/a+y/b=2, ax-by=a^2-b^2

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  21. Word Problem of Numbers A number between 10 and 100 is equal to eigh...

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