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If x= (7+4sqrt(3)), prove that x+1//x= 1...

If `x= (7+4sqrt(3)),` prove that `x+1//x`= 14

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CENGAGE PUBLICATION-COMPLEX NUMBERS AND QUADRATIC EQUATIONS-All Questions
  1. Solve sqrt(3x^2-7x-30)-sqrt(2x^2-7x-5)=x-5.

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  2. If the cube roots of unity are 1,omega,omega^2, then the roots of the ...

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  3. If x= (7+4sqrt(3)), prove that x+1//x= 14

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  4. Prove that the locus of midpoint of line segment intercepted between ...

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  5. Solve sqrt(5x^2-6x+8)+sqrt(5x^2-6x-7)=1.

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  6. Show that: sum(r=0)^(n-1)|z1+alpha^r z2|^2=n(|z1|^2+|z2|^2),w h e r e,...

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  7. Solve sqrt(x^2+4x-21)+sqrt(x^2-x-6)=sqrt(6x^2-5x-39.)

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  8. If alpha=(z-i)/(z+i), show that, when z lies above the real axis, alph...

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  9. Solve 4^x+6^x=9^xdot

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  10. Let x1, x2 are the roots of the quadratic equation x^2+a x+b=0,w h e r...

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  11. Solve 3^(2x^2-7x+7)=9.

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  12. Plot the region represented by pi/3lt=a r g((z+1)/(z-1))lt=(2pi)/3 in ...

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  13. How many solutions does the equation(8^x + 27^x)/(12^x +18^x) = 7/6hav...

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  14. Is the following computation correct? If not give the correct compu...

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  15. Consider an equilateral triangle having verticals at point A(2/sqrt3 e...

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  16. Find the number of real roots of the equation (x-1)^2+(x-2)^2+(x-3)^2=...

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  17. Find the value of (i^(592)+i^(590)+i^(588)+i^(586)+i^(584))/(i^(582)+i...

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  18. Let z,z(0) be two complex numbers. It is given that abs(z)=1 and the n...

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  19. Show that the equation a z^3+b z^2+ barb z+ bara =0 has a root alpha ...

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  20. If nge3and1,alpha(1),alpha(2),alpha(3),...,alpha(n-1) are the n,nth ...

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