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Question Number 175925 Answers: 1 Comments: 1

1^x +6^x +8^x =9^x find x ? Mastermind

$$\mathrm{1}^{\mathrm{x}} +\mathrm{6}^{\mathrm{x}} +\mathrm{8}^{\mathrm{x}} =\mathrm{9}^{\mathrm{x}} \\ $$$$\mathrm{find}\:\mathrm{x}\:? \\ $$$$ \\ $$$$\mathrm{Mastermind} \\ $$

Question Number 175916 Answers: 1 Comments: 1

f(x)= 2^( (( sin(x) +(√3) cos(x)))^(1/3) ) − 2^( ((−sin(x) −(√3) cos(x)))^(1/3) ) R_( f) =?

$$ \\ $$$$\:\:\:\:{f}\left({x}\right)=\:\mathrm{2}^{\:\sqrt[{\mathrm{3}}]{\:{sin}\left({x}\right)\:+\sqrt{\mathrm{3}}\:{cos}\left({x}\right)}\:} −\:\mathrm{2}^{\:\sqrt[{\mathrm{3}}]{−{sin}\left({x}\right)\:−\sqrt{\mathrm{3}}\:{cos}\left({x}\right)}} \\ $$$$\:\:\:\:\:\:\:{R}_{\:{f}} \:=? \\ $$

Question Number 175904 Answers: 2 Comments: 1

If 1 + sinx + sin^2 x + sin^3 x + ........ ∞ = 4 + 2(√3), x = ?

$$ \\ $$$$\mathrm{If}\:\:\mathrm{1}\:+\:{sinx}\:+\:{sin}^{\mathrm{2}} {x}\:+\:{sin}^{\mathrm{3}} {x}\:+\:........\:\infty\:\:\:=\:\:\mathrm{4}\:+\:\mathrm{2}\sqrt{\mathrm{3}},\: \\ $$$${x}\:=\:? \\ $$

Question Number 175901 Answers: 2 Comments: 1

Question Number 175894 Answers: 1 Comments: 0

Question Number 175888 Answers: 1 Comments: 0

Solve the differential equation (dy/dx)=((1+y^2 )/(y(1−x^2 )))

$$\mathrm{Solve}\:\mathrm{the}\:\mathrm{differential}\:\mathrm{equation} \\ $$$$\frac{\mathrm{dy}}{\mathrm{dx}}=\frac{\mathrm{1}+\mathrm{y}^{\mathrm{2}} }{\mathrm{y}\left(\mathrm{1}−\mathrm{x}^{\mathrm{2}} \right)} \\ $$

Question Number 175893 Answers: 1 Comments: 3

If outer angle in n−polygone is 18° find n

$$\:{If}\:{outer}\:{angle}\:{in}\:{n}−{polygone}\:{is}\:\mathrm{18}° \\ $$$$\:{find}\:{n} \\ $$

Question Number 175880 Answers: 1 Comments: 0

Question Number 175879 Answers: 0 Comments: 2

If cos x .(dy/dx) = y ⇒y((π/3))=?

$$\:\:\mathrm{If}\:\mathrm{cos}\:\mathrm{x}\:.\frac{\mathrm{dy}}{\mathrm{dx}}\:=\:\mathrm{y}\:\Rightarrow\mathrm{y}\left(\frac{\pi}{\mathrm{3}}\right)=? \\ $$

Question Number 175871 Answers: 2 Comments: 0

f(x) = (√(x^2 −4x+13)) + (√(x^2 −14x+130)) minimum value of f(x) x ∈ R

$$\:\:\mathrm{f}\left(\mathrm{x}\right)\:=\:\sqrt{\mathrm{x}^{\mathrm{2}} −\mathrm{4x}+\mathrm{13}}\:+\:\sqrt{\mathrm{x}^{\mathrm{2}} −\mathrm{14x}+\mathrm{130}} \\ $$$$\:\mathrm{minimum}\:\mathrm{value}\:\mathrm{of}\:\:\mathrm{f}\left(\mathrm{x}\right)\:\:\mathrm{x}\:\in\:\mathbb{R}\: \\ $$

Question Number 175866 Answers: 1 Comments: 0

f(x)=x^3 +ax f^(−1) (x)=?

$${f}\left({x}\right)={x}^{\mathrm{3}} +{ax} \\ $$$${f}^{−\mathrm{1}} \left({x}\right)=? \\ $$

Question Number 175863 Answers: 0 Comments: 0

Question Number 175860 Answers: 2 Comments: 0

Question Number 175849 Answers: 2 Comments: 0

2^(2a) +2^a = 10 what is a?

$$\mathrm{2}^{\mathrm{2}{a}} +\mathrm{2}^{{a}} =\:\mathrm{10} \\ $$$${what}\:{is}\:{a}? \\ $$

Question Number 175839 Answers: 2 Comments: 0

If w, x, y and z be four consecutive terms of any AP, then show that w^2 −z^2 =3(x^2 −y^2 ).

$${If}\:{w},\:{x},\:{y}\:{and}\:{z}\:{be}\:{four}\:{consecutive} \\ $$$${terms}\:{of}\:{any}\:{AP},\:{then}\:{show}\:{that} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:{w}^{\mathrm{2}} −{z}^{\mathrm{2}} =\mathrm{3}\left({x}^{\mathrm{2}} −{y}^{\mathrm{2}} \right). \\ $$

Question Number 175838 Answers: 2 Comments: 0

If x,y and z be the pth, qth and rth terms of an AP, show that determinant ((p,q,r),(x,y,z),(1,1,1))=0

$${If}\:{x},{y}\:{and}\:{z}\:{be}\:{the}\:{pth},\:{qth}\:{and}\:{rth} \\ $$$${terms}\:{of}\:{an}\:{AP},\:{show}\:{that} \\ $$$$\begin{vmatrix}{{p}}&{{q}}&{{r}}\\{{x}}&{{y}}&{{z}}\\{\mathrm{1}}&{\mathrm{1}}&{\mathrm{1}}\end{vmatrix}=\mathrm{0} \\ $$

Question Number 175836 Answers: 2 Comments: 1

Question Number 175834 Answers: 0 Comments: 4

xe^x^(1/) = e solve for x

$${xe}^{\overset{\mathrm{1}/} {{x}}} =\:{e} \\ $$$${solve}\:{for}\:{x} \\ $$

Question Number 175833 Answers: 0 Comments: 0

Question Number 176750 Answers: 0 Comments: 2

Is there general form of α^n + β^n and α^n − β^n ???? e.g: α^3 + β^3 = (α + β)[(α + β)^2 − 3αβ]

$$\mathrm{Is}\:\mathrm{there}\:\mathrm{general}\:\mathrm{form}\:\mathrm{of} \\ $$$$\alpha^{\mathrm{n}} \:\:\:+\:\:\:\beta^{\mathrm{n}} \:\:\:\:\:\mathrm{and}\:\:\:\:\:\:\alpha^{\mathrm{n}} \:\:\:−\:\:\:\beta^{\mathrm{n}} \:\:\:\:\:???? \\ $$$$ \\ $$$$\mathrm{e}.\mathrm{g}:\:\:\:\:\alpha^{\mathrm{3}} \:\:\:+\:\:\:\beta^{\mathrm{3}} \:\:\:\:=\:\:\:\:\left(\alpha\:\:\:+\:\:\:\beta\right)\left[\left(\alpha\:\:\:+\:\:\:\beta\right)^{\mathrm{2}} \:\:\:−\:\:\:\mathrm{3}\alpha\beta\right] \\ $$

Question Number 175829 Answers: 2 Comments: 0

The 2^(nd) term of a Geometric Progresion (G.P) is equal to the 8^(th) term of an Arithmetic Progresion (A.P). The first terms, common difference and common ratio are all equal and non−zero. Find the sum of the first five terms of the Geometric Progresion(G.P)

$$\mathrm{The}\:\mathrm{2}^{\mathrm{nd}} \:\mathrm{term}\:\mathrm{of}\:\mathrm{a}\:\mathrm{Geometric}\:\mathrm{Progresion} \\ $$$$\left(\mathrm{G}.\mathrm{P}\right)\:\mathrm{is}\:\mathrm{equal}\:\mathrm{to}\:\mathrm{the}\:\mathrm{8}^{\mathrm{th}} \:\mathrm{term}\:\mathrm{of}\:\mathrm{an}\:\mathrm{Arithmetic} \\ $$$$\mathrm{Progresion}\:\left(\mathrm{A}.\mathrm{P}\right).\:\mathrm{The}\:\mathrm{first}\:\mathrm{terms},\:\mathrm{common} \\ $$$$\mathrm{difference}\:\mathrm{and}\:\mathrm{common}\:\mathrm{ratio}\:\mathrm{are}\:\mathrm{all}\:\mathrm{equal} \\ $$$$\mathrm{and}\:\mathrm{non}−\mathrm{zero}.\:\mathrm{Find}\:\mathrm{the}\:\mathrm{sum}\:\mathrm{of}\:\mathrm{the}\:\mathrm{first}\:\mathrm{five} \\ $$$$\mathrm{terms}\:\mathrm{of}\:\mathrm{the}\:\mathrm{Geometric}\:\mathrm{Progresion}\left(\mathrm{G}.\mathrm{P}\right) \\ $$

Question Number 175827 Answers: 0 Comments: 4

Question Number 175821 Answers: 1 Comments: 1

Question Number 175815 Answers: 2 Comments: 0

If n≥1 a and b are positive real numbers Then prove that: ((a^n + b^n )/(a + b)) ≥ ((a^(n−1) + b^(n−1) )/2)

$$\mathrm{If}\:\:\:\mathrm{n}\geqslant\mathrm{1} \\ $$$$\:\:\:\:\:\:\:\mathrm{a}\:\mathrm{and}\:\mathrm{b}\:\mathrm{are}\:\mathrm{positive}\:\mathrm{real}\:\mathrm{numbers} \\ $$$$\mathrm{Then}\:\mathrm{prove}\:\mathrm{that}: \\ $$$$\frac{\mathrm{a}^{\boldsymbol{\mathrm{n}}} \:\:+\:\:\mathrm{b}^{\boldsymbol{\mathrm{n}}} }{\mathrm{a}\:\:+\:\:\mathrm{b}}\:\:\geqslant\:\:\frac{\mathrm{a}^{\boldsymbol{\mathrm{n}}−\mathrm{1}} \:\:+\:\:\mathrm{b}^{\boldsymbol{\mathrm{n}}−\mathrm{1}} }{\mathrm{2}} \\ $$

Question Number 175814 Answers: 2 Comments: 1

Question Number 175806 Answers: 1 Comments: 0

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