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Solve: (14)/(x+3)-1=(5)/(x+1),xne-3,-1....

Solve: `(14)/(x+3)-1=(5)/(x+1),xne-3,-1.`

Text Solution

Verified by Experts

The given equation may be written as
`(14)/(x+3)-(5)/(x+1)=1`
`implies" "(14(x+1)-5(x+3))/((x+3)(x+1))=1`
`implies" "((9x-1))/(x^(2)+4x+3)=1impliesx^(2)+4x+3=9x-1`
`implies" "x^(2)-5x+4=0impliesx^(2)-4x-x+4=0`
`implies" "x(x-4)-(x-4)=0implies(x-4)(x-1)=0`
`implies" "x-4=0" or "x-1=0`
`implies" "x=4" or "x=1.`
Hence, 4 and 1 are the roots of the given equation.
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RS AGGARWAL-QUADRATIC EQUATIONS -Test Yourself
  1. Solve: (14)/(x+3)-1=(5)/(x+1),xne-3,-1.

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  2. Which of the following is a quadratic equation?

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  3. Which of the following is a quadratic equation ?

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  4. Which of the following is not a quadratic equation?

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  5. If x=3 is a solution of the equation 3x^(2)+(k-1)x+9=0 then k=?

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  6. If one root of the equation 2x^(2)+ax+6=0 is 2 then a=?

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  7. The sum of the roots of the equation x^(2)-6x+2=0 is

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  8. If the product of the roots of the equation x^(2)-3x+k=10 is -2 then t...

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  9. The ratio of the sum and product of the roots of the equation 7x^(2)-1...

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  10. If one root of the equation 3x^(2)-10x+3=0" is "(1)/(3) then the other...

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  11. If one root of 5x^(2)+13x+k=0 be the reciprocal of the other root then...

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  12. If the sum of the roots of the equation kx^(2)+2x+3k=0 is equal to the...

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  13. The roots of a quadratic equation are 5 and -2. Then, the equation is

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  14. If the sum of the roots of aquadratic equation is 6 and their product...

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  15. If alpha and beta are the roots of the equation 3x^(2)+8x+2=0 then ((1...

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  16. The roots of the equation ax^(2)+bx+c=0 will be reciprocal of each oth...

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  17. If the roots of the equation ax^(2)+bx+c=0 are equal then c=?

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  18. If the equation 9x^(2)+6kx+4=0 has equal roots then k=?

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  19. If the equation x^(2)+2(k+2)x+9k=0 has equal roots then k= ?

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  20. If the equation 4x^(2)-3kx+1=0 has equal roots then k=?

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  21. The roots of ax^(2)+bx+c=0, ane0 are real and unequal, if (b^(2)-4ac)

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