Bissoy.com
Doctors Medicines MCQs Q&A

Let ω and ω2 be the non-real cube roots of unity and 1/(a+ω)+1/(b+ω)+1/(c+ω)=2ω2 and 1/(a+ω2)+1/(b+ω2)+1/(c+ω2)=2ω, then calculate 1/(a+1)+1/(b+1)+1/(c+1).

Let ω and ω2 be the non-real cube roots of unity and 1/(a+ω)+1/(b+ω)+1/(c+ω)=2ω2 and 1/(a+ω2)+1/(b+ω2)+1/(c+ω2)=2ω, then calculate 1/(a+1)+1/(b+1)+1/(c+1). Correct Answer 2

Given relations can be written as: 1/(a+ω)+1/(b+ω)+1/(c+ω)=2/ω, and 1/(a+ω2)+1/(b+ω2)+1/(c+ω2)=2/ω2⇒ω and ω2 are roots of 1/(a+x)+1/(b+x)+1/(c+x)=2/x. ⇒/=2/x⇒x3+(bc+ca+ab)x-2abc=0. Let 3rd root be α (apart from ω and ω2). Then, α+ ω+ ω2=coefficient of x2=0⇒α=1. Hence, 1/(a+1)+1/(b+1)+1/(c+1)=2/1=2.

Related Questions

The accompanying image shows a large cube made of dark and white small sugar cubes. Small cubes of the diagonally arranged row of the bottom surface of the large cube, small cubes of the row with one face on the right-hand surface of the large cube, small cubes of the row with one face on the front surface of the large cube, and small cubes of the column with one face on the top of large cube surface are all dark. Select the number of small white cubes of the large cube.
Given below are two statements, followed by four conclusions. Assume the facts in the statements to be true and decide which of the conclusions logically follow(s) from the statements. Statements: All roots are fruits. All fruits are guns. Conclusions: I. All roots are guns,. II. All guns are roots. III. All fruits are roots. IV. Some guns are roots.
Read the given statements and conclusions carefully. Assuming that the information given in the statements is true, even if it appears to be at variance with commonly known facts, decide which of the given conclusions logically follow(s) from the statements. Statements: All woods are roots. All fruits are roots. No woods are a fruit. Conclusion: (I) Some roots are fruits. (II) All roots are woods.
Let a and b be complex cube roots of unity. If x=7a+2b and y=2a+7b, then evaluate xy.
Consider a circle with centre at O and radius 7 cm. Let QR be the chord of length 2 cm and let P be the midpoint of QR. Let CD be another chord of this circle passing through P such that ∠CPQ is acute. If M is the midpoint of CD and MP = √24 cm, then which of the following statements are correct? (1) ∠QPD = 135° (2) If CP = m cm and PD = n cm, then m and n are the roots of the quadratic equation x2 – 10x + 1 = 0 (3) The ratio of triangle OPR to the area of triangle OMP is 1 ∶ 2√2 Select the correct answer using the code given below.
The ratio of volumes of two cubes X and Y is ratio 8 ∶ 3. If the total surface area of cube X is increased by 44% and that of cube Y is decreased by 36%, then what is the ratio of the new volume of the cube X to that of cube Y?
A cone of maximum volume is cut from the cube of total surface area 2646 cm2 is such a way that one face of the cube becomes base of the cone and vertex of the cone touches opposite face of cube, then what will be the volume of remaining volume of cube after cutting the cone from it?
A large cube is kept on a table. If 5 cuts parallel to the surface are made on the cube without putting one cube over the other, then in how many maximum pieces can the cube be thus broken?
The ratio of the length of diagonal of two cubes is 2 ∶ 3 and the difference between the total surface area of the bigger cube and the lateral surface area of the smaller cube is 342 cm2. Find the total surface area of a statue which is formed by placing the smaller cube upon the bigger cube.
A right circular cone is exactly fitted inside a cube in such a way that the edges of the base of the cone are touching the edge of one of the face of the cube and the vertex is on the opposite face of the cube. If the volume of the cube is 9261 cm3, what is the volume of the cone?