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If a,b,c are real, `a ne 0, b ne 0, c ne 0` and `a+b + c ne 0` and `1/a + 1/b + 1/c = 1/(a+b+c)` , then `(a+b) (b+c)(c+a)`=

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RESONANCE ENGLISH-EQUATIONS -EXERCISE-1 (PART -1: PRE RMO)
  1. The number of integer values of a for which x^2+ 3ax + 2009 = 0 has tw...

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  2. The sum of the fourth powers of the roots of the equation x^(3)- x^(2)...

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  3. If a,b,c are real, a ne 0, b ne 0, c ne 0 and a+b + c ne 0 and 1/a + 1...

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  4. If the roots x^5-40 x^4+P x^3+Q x^2+R x+S=0 are n G.P. and the sum of ...

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  5. The number of solutions (x, y) where x and y are integers, satisfying ...

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  6. If p/a + q/b + r/c=1 and a/p + b/q + c/r=0, then the value of p^(2)/a^...

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  7. A cubic polynomial P is such that P(1) = 1, P(2) = 2, P(3) = 3 and P(4...

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  8. Which of the following is the best approximation to ((2^(3)-1) (3^(3)-...

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  9. Given that (1-x) (1+x+x^(2) +x^(3) +x^(4)) = 31/32 and x is a rational...

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  10. Solve the equation 3x^(4) -10x^(3) + 4x^(2) -x-6=0 one root being (1+s...

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  11. Find the smallest integral x satisfying the inequality (x-5)/(x^(2) + ...

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  12. Find integral 'x's which satisfy the inequality x^(4) -3x^(3) -x +3 lt...

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  13. Find the largest integral x which satisfies the following inequality: ...

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  14. Given 3x^(2) +x=1, find the value of 6x^(3) - x^(2) -3x + 2010.

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  15. If 1/x - 1/y=4, find the value of (2x+4xy-2y)/(x-y-2xy).

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  16. Let f(x)=ax^(7)+bx^(3)+cx-5where a,b and c are constants. If f(-7)=7, ...

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  17. If xy = a, xz = b, yz = c and abc ne 0, find the value of x^2 + y^2 +...

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  18. Find the number of positive integers x satisfying the equation 1/x + 1...

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  19. Solve the following equation: (x-1) (x-2)(x-3)(x-4)=15

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  20. Solve the following equation : (x^(2)-3.5 x + 1.5)/(x^(2)-x-6)=0

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