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Find the positive solutions of the syste...

Find the positive solutions of the system of equations `x^(x+y)=y^n and y(x+y)= 2^(2n. Y^n, where ngt0`

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A DAS GUPTA-Equations, Inequation and Expressions-Exercise
  1. Let {x} and [x] denote the fractional and integral part of a real numb...

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  2. If x,y,z are positive intergers and x+y+z=240 and x^2 + y^2= z^2 then ...

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  3. Find the positive solutions of the system of equations x^(x+y)=y^n and...

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  4. Solve the equations log1000 |x+y| = 1/2 . log10 y - log10 |x| = log100...

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  5. Find all values of theta in the interva (-pi/2,pi/2) satisfying the eq...

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  6. Find the set of all real 'a' such that 5a^(2)-3a-2,a^(2)+a-2 and 2a^(2...

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  7. Solve (x+3)^(2)-(x-1)^(5)ge244.

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  8. Let sqrt(((x+1)(x-3))/((x-2))). Find all the real values of x for whic...

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  9. Let f(x)= (2x)/(2x^2+5x+2) and g(x)=1/(x+1). Find the set of real valu...

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  10. 1 < (3 x^2 - 7x + 8)/(x^2 + 1) <2

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  11. Solve for x in R : 4^(x^2)=< 3.2^(x^2+2)+ 4^(x+1).

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  12. Solve abs(x-1) + abs(x-2) + abs(x-3)ge 6, x in R.

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  13. Solve abs(abs(x-2)-1) ge 3.

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  14. If x=4/9 satisfies the equation (log)a(x^2-x+2)>(log)a(-x^2+2x+3), the...

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  15. If log(3x+5)(a x^2+8x+2)>2 then x lies in the interval

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  16. Let there be a quotient of two natural numbers in which the derin whic...

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  17. If p and q are odd integers the equation x^2 + 2px + 2q = 0 cannot hav...

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  18. If the roots of x^2-ax+b=0 are real and differ by a quantity which is ...

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  19. If altbltcltd the equation (x-a)(x-c)+lambda(x-b)(x-d)=0 has real root...

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  20. If p is the first of the n arithmetic means between two numbers and q ...

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