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Solve: (2)/((x+1))+(3)/(2(x-2))=(23)/(5x...

Solve: `(2)/((x+1))+(3)/(2(x-2))=(23)/(5x),xne0,-1,2.`

A

`5, -19/11`

B

`6, 14/11`

C

`4, -23/11`

D

`5, -13/11`

Text Solution

Verified by Experts

The correct Answer is:
C
We have
`(2)/((x+1))+(3)/(2(x-2))=(23)/(5x)`
`implies" "(4(x-2)+3(x+1))/(2(x+1)(x-2))=(23)/(5x)implies(7x-5)/(2(x^(2)-x-2))=(23)/(5x)`
`implies" "5x(7x-5)=46(x^(2)-x-2)" "["by cross multiplication"]`
`implies35x^(2)-25x=46x^(2)-46x-92`
`implies" "11x^(2)-21x-92=0implies11x^(2)-44x+23x-92=0`
`implies" "11x(x-4)+23(x-4)=0implies(x-4)(11x+23)=0`
`implies" "x-4=0" or "11x+23=0`
`implies" "x=4" or "x=(-23)/(11).`
Hence, 4 and `(-23)/(11)` are the roots of the given equation.
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RS AGGARWAL-QUADRATIC EQUATIONS -Test Yourself
  1. Solve: (2)/((x+1))+(3)/(2(x-2))=(23)/(5x),xne0,-1,2.

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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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  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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