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If a>1, prove that the solutions of the ...

If `a>1`, prove that the solutions of the following equation in x is independent of a. `(a+ sqrt(a^2-1))^(x^2-2x)+ (a-sqrt(a^2-1))^(x^2-2x)= 2a`.

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A DAS GUPTA-Equations, Inequation and Expressions-Exercise
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  2. Solve (sqrt3+1)^(2x)+(sqrt3-1)^(2x)=2^(3x).

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  3. If a>1, prove that the solutions of the following equation in x is ind...

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  6. Solve 25^(log(10)x)=5+4x^(log(10)5)

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  7. Solve |x^2+4x+3|+2x+5=0.

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  8. For a alt=0, determine all real roots of the equation x^2-2a|x-a|-3...

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  9. Solve (x+2)^2 -3 abs(x+2)+2=0 .

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  10. Solve abs(x+1)+ abs(x-1) =2.

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  11. log(|x+6|) 2 . log2 (x^2-x-2) >= 1

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  12. The set of real values of x satisfying the equation |x-1|^(log3(x^2)-...

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  13. Let {x} and [x] denote the fractional and integral part of a real numb...

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

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

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

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

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

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

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