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If the real numbers x, y, z are such that `x^2 + 4y^2 + 16z^2 = 48` and `xy + 4yz + 2zx = 24`. what is the value of `x^(2) +y^(2) z^(2)`=?

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RESONANCE ENGLISH-EQUATIONS -EXERCISE-2 (PART-I: PREVIOUS ASKED QUESTION FOR PRE RMO)
  1. What is the smallest possible natural number 'n' for which the equatio...

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  2. Natural numbers k,l,p and q are such that if a and b are roots of x^(2...

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  3. If real numbers a, b, c, d, e satisfy a+1=b + 2 = c+ 3 = d + 4 = e + 5...

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  4. The equations x^2 - 4x + k = 0 and x^2 + kx -4 = 0 where k is a real n...

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  5. Let a, b and c be real numbers such that a - 7b + 8c = 4 and 8a + 4b -...

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  6. Let a, b and c be such that a + b + c= 0 and P=a^(2)/(2a^(2)+ bc) + b^...

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  7. Suppose x^(2)-x +1 is factor of 2x^(6) - x^(5) + ax^(4) + x^(3)+bx^(2)...

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  8. For how many pairs of odd positive integers (a, b), both a, b less tha...

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  9. Find the sum of all those integers n for which n^2+20n+15 is the squar...

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  10. Let a and p be the roots of equation x^2 + x - 3 = 0. Find the value o...

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  11. For real numbers x and y, let M be the maximum value of expression x^4...

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  12. Between 5pm and 6pm, I looked at my watch mistaking the hour hand for ...

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  13. Suppose a, b are positive real numbers such that asqrt(a) + b sqrt(b) ...

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  14. Let a, b be integers such that all the roots of the equation (x^2 + ax...

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  15. In a class, the total numbers of boys and girls are in the ratio 4 : 3...

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  16. If the real numbers x, y, z are such that x^2 + 4y^2 + 16z^2 = 48 and ...

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  17. Suppose 1,2,3 are the roots of the equation x^4 + ax^2 + bx + c = 0. ...

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  18. Determine the sum of all possible positive integers n, the product of ...

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  19. Suppose a, b are integers and a + b is a root of x^2 + ax + b = 0. Wha...

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  20. Integers a, b, c satisfy a + b - c = 1 and a^2 + b^2 - c^2 = -1. What ...

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