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If the roots of the equation ax^2+bx+c=0...

If the roots of the equation `ax^2+bx+c=0` are `alpha` and `beta` then show that `1/(a alpha+b)+1/(abeta+b)=b/(ac)`.

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UNITED BOOK HOUSE-MISCELLANEOUS EXERCISE-EXERCISE
  1. If the roots of the equation a(b-c)x^2+b(c-a)x+c(a-b)=0 are equal,the...

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  2. If the difference of the roots of the equation x^2-px+q=0 is 1, then s...

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  3. If the roots of the equation ax^2+bx+c=0 are alpha and beta then show ...

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  4. If (a+b+c)p=(b+c-a)q=(c+a-b)r=(a+b-c)s, then show that qrs= p(qr+rs+qs...

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  5. If a+1/b = 1, b+1/c = 1, then show that abc+1 = 0

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  6. If (x^2-yz)/a=(y^2-zx)/b=(z^2-xy)/c , show that (a+b+c)(x+y+z)=(ax+by...

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  7. If ax^2+bxy+cy^2 =0 , find x:y.

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  8. 6 is the mean proportional between two numbers x ad y and 48 is the th...

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  9. If (x^3+3xy^2)/(y^3+3x^2y)= 63/62 show that x:y = 3:2.

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  10. If (a+c):(b+c) = (a/b+2):(b/a+2) then show that (a-c):(b-c) = a^2:b^2.

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  11. If (5a-3b)/a= (4a+b-2c)/(a+4b-2c) = (a+2b-3c)/(4a-4c), then show that ...

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  12. If (x+y+z)(y+z-x)(z+x-y)(x+y-z) prop x^2y^2 then show that either x^2+...

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  13. If 1/x-1/y prop 1/(y-x) then show that x/y is constant.

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  14. Simplify: 1/sqrt(11-2sqrt(30))-3/(sqrt7-2sqrt(10))-4/(sqrt(8+4sqrt3))

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  15. Find the square roots of- 8+2sqrt2-2sqrt5-2sqrt(10)

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  16. Find the square roots of- 1+x^2+ sqrt(1+x^2+x^4)

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  17. If 2x = sqrta+1/sqrta. Show that sqrt(x^2-1)/(x-sqrt(x^2-1))(a-1)

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  18. If (x+sqrt(x^2-bc))(y+sqrt(y^2-ca))(z+sqrt(z^2-ab)) = (x-sqrt(x^2-bc...

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  19. If x = (sqrt(a^2+b^2)+sqrt(a^2-b^2))/(sqrt(a^2+b^2)-sqrt(a^2-b^2)) sho...

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  20. If x>y prove that sqrt(y+sqrt(2xy-x^2))+sqrt(y-sqrt(2xy-x^2)) = sqrt(...

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