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Question Number 202058 Answers: 1 Comments: 1

Solve by computer programming a, b & c are Prime numbers. And they are in AP and d is common difference Example (a, b, c, d) = (3, 5, 7, 2) Just Next Set(a, b, c, d) = ?

$$\mathrm{Solve}\:\mathrm{by}\:\mathrm{computer}\:\mathrm{programming} \\ $$$${a},\:{b}\:\&\:{c}\:{are}\:{Prime}\:{numbers}.\:\mathrm{And}\:\mathrm{they} \\ $$$$\:\mathrm{are}\:\mathrm{in}\:\mathrm{AP}\:\mathrm{and}\:\mathrm{d}\:\mathrm{is}\:\mathrm{common}\:\mathrm{difference} \\ $$$$\mathrm{Example}\:\left(\mathrm{a},\:\mathrm{b},\:\mathrm{c},\:\mathrm{d}\right)\:=\:\left(\mathrm{3},\:\mathrm{5},\:\mathrm{7},\:\mathrm{2}\right) \\ $$$$\:\mathrm{Just}\:\mathrm{Next}\:\mathrm{Set}\left(\mathrm{a},\:\mathrm{b},\:\mathrm{c},\:\mathrm{d}\right)\:=\:? \\ $$

Question Number 202056 Answers: 0 Comments: 9

Question Number 202044 Answers: 2 Comments: 1

If a = 9999999998000000001 Find A = (((√a) + 1))^(1/9) → A = ?

$$\mathrm{If} \\ $$$$\mathrm{a}\:=\:\mathrm{9999999998000000001} \\ $$$$\mathrm{Find} \\ $$$$\mathrm{A}\:=\:\sqrt[{\mathrm{9}}]{\sqrt{\mathrm{a}}\:+\:\mathrm{1}}\:\:\:\rightarrow\:\:\:\mathrm{A}\:=\:? \\ $$

Question Number 202041 Answers: 1 Comments: 0

Simplify: (((√2) − sinα − cosα)/(sinα − cosα))

$$\mathrm{Simplify}:\:\:\:\frac{\sqrt{\mathrm{2}}\:−\:\mathrm{sin}\alpha\:−\:\mathrm{cos}\alpha}{\mathrm{sin}\alpha\:−\:\mathrm{cos}\alpha} \\ $$

Question Number 202034 Answers: 1 Comments: 0

Question Number 202039 Answers: 1 Comments: 0

Question Number 202037 Answers: 1 Comments: 0

A board has 2, 4, and 6 written on it. One repeatedly chooses values (not necessarily different) for x, y, and z from the board, and writes xyz + xy + yz + zx + x + y + z if and only if those numbers are not already on the board and are also less than or equals 2013. The person repeats this process until no more numbers can be written. How many numbers will be written at the end of this process?

$$ \\ $$A board has 2, 4, and 6 written on it. One repeatedly chooses values (not necessarily different) for x, y, and z from the board, and writes xyz + xy + yz + zx + x + y + z if and only if those numbers are not already on the board and are also less than or equals 2013. The person repeats this process until no more numbers can be written. How many numbers will be written at the end of this process?

Question Number 202035 Answers: 0 Comments: 0

Question Number 202019 Answers: 3 Comments: 0

If α and β are the roots of the ax^2 + 2bx + c = 0 and α + δ and β + δ are the roots of Ax^2 + 2Bx + C = 0 for some constant δ then prove that ((b^2 − ac)/a^2 ) = ((B^2 − AC)/A^2 ) .

$$\mathrm{If}\:\alpha\:\mathrm{and}\:\beta\:\mathrm{are}\:\mathrm{the}\:\mathrm{roots}\:\mathrm{of}\:\mathrm{the}\: \\ $$$${ax}^{\mathrm{2}} \:+\:\mathrm{2}{bx}\:+\:{c}\:=\:\mathrm{0}\:\mathrm{and}\:\alpha\:+\:\delta\:\mathrm{and}\:\beta\:+\:\delta\:\mathrm{are} \\ $$$$\mathrm{the}\:\mathrm{roots}\:\mathrm{of}\:{Ax}^{\mathrm{2}} \:+\:\mathrm{2}{Bx}\:+\:{C}\:=\:\mathrm{0}\:\mathrm{for}\:\mathrm{some}\: \\ $$$$\mathrm{constant}\:\delta\:\mathrm{then}\:\mathrm{prove}\:\mathrm{that} \\ $$$$\frac{{b}^{\mathrm{2}} \:−\:{ac}}{{a}^{\mathrm{2}} }\:=\:\frac{{B}^{\mathrm{2}} \:−\:{AC}}{{A}^{\mathrm{2}} }\:. \\ $$

Question Number 202017 Answers: 3 Comments: 0