Roots of x²+2x+2=0 — Find α¹⁵+β¹⁵
If α, β are the roots of x²+2x+2=0, find α¹⁵+β¹⁵ by converting the complex roots to polar form and using De Moivre’s theorem.
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Three Circles of Radii a, b, c Touch Externally With x-axis as Common Tangent
Three circles of radii a, b, c touch each other externally with the x-axis as a common tangent. Derive the relation between a, b, c using centre coordinates and distance.
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Sum of 1 + 6 + 9(1²+2²+3²)/7 + 12(1²+2²+3²+4²)/9 + … Up to 15 Terms
The sum of the series 1+6+9(1²+2²+3²)/7+12(1²+2²+3²+4²)/9+15(1²+…+5²)/11+… up to 15 terms is: (1)7820 (2)7520 (3)7830 (4)7510.