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If a, b, c are positive integers such th...

If a, b, c are positive integers such that `a^2+ 2b^2-2ab = 169` and `2bc - c^2= 169` then a + b + c is:

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RESONANCE-EQUATIONS -EXERCISE-1 (PART -1: PRE RMO)
  1. The remainder obtained when the polynomial x+x^(3)+x^(9)+x^(27)+x^(81)...

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  2. If x, y are positive real numbers satisfying the system of equations x...

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  3. If a, b, c are positive integers such that a^2+ 2b^2-2ab = 169 and 2bc...

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  4. P = 2008^(2007) - 2008, Q = 2008^(2) + 2009. The remainder when P is d...

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  5. The number of integer values of a for which x^2+ 3ax + 2009 = 0 has tw...

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

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  7. If the roots of x^(5) - 40 x^(4) + Px^(3) + Qx^(2) + Rx + S = 0 are in...

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

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  9. If (p )/(a) + (q)/(b) = (r)/(c) = 1 and (a )/(p )+ (b)/(q) + (c)/(r) =...

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

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

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

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

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

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

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

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

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

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  19. Let P(x) =ax^(7) + bx^(3) +cx-5, where a,b,c are constants. Given P(-7...

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

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