Question and Answers Forum

AlgebraQuestion and Answers: Page 236

Question Number 120960 Answers: 0 Comments: 0

If x,y,z>0 then prove following inequality (x^2 +2)(y^2 +2)(z^2 +2)≥9(xy+yz+xz)

$${If}\:{x},{y},{z}>\mathrm{0}\:\:{then}\:{prove}\:{following} \\ $$$${inequality} \\ $$$$\left({x}^{\mathrm{2}} +\mathrm{2}\right)\left({y}^{\mathrm{2}} +\mathrm{2}\right)\left({z}^{\mathrm{2}} +\mathrm{2}\right)\geqslant\mathrm{9}\left({xy}+{yz}+{xz}\right) \\ $$

Question Number 120953 Answers: 4 Comments: 0

solve in x∈R ∣ 3x−4 ∣ = x−5

$$\mathrm{solve}\:\mathrm{in}\:\mathrm{x}\in\mathbb{R} \\ $$$$\mid\:\mathrm{3x}−\mathrm{4}\:\mid\:=\:\mathrm{x}−\mathrm{5}\: \\ $$

Question Number 120943 Answers: 3 Comments: 1

∫(x^3 +3)^4 dx=?

$$\int\left({x}^{\mathrm{3}} +\mathrm{3}\right)^{\mathrm{4}} {dx}=? \\ $$

Question Number 120929 Answers: 5 Comments: 2

Question Number 120904 Answers: 1 Comments: 1

Question Number 120882 Answers: 1 Comments: 0

Question Number 120855 Answers: 2 Comments: 0

... elementary calculus... :: α,β are roots of equation of : x^2 −6x−2=0 define :: t_n =α^n −β^n (n≥1) then evaluate : A=((t_(10) −2t_8 )/(2t_9 )) =??? ...m.n.1970...

$$\:\:\:\:\:\:\:\:\:\:\:...\:{elementary}\:\:{calculus}... \\ $$$$\:\:::\:\alpha,\beta\:{are}\:{roots}\:{of}\:\:{equation} \\ $$$$\:\:\:\:\:{of}\::\:{x}^{\mathrm{2}} −\mathrm{6}{x}−\mathrm{2}=\mathrm{0} \\ $$$$\:\:\:\:\:\:\:\:\:{define}\:::\:{t}_{{n}} =\alpha^{{n}} −\beta^{{n}} \:\left({n}\geqslant\mathrm{1}\right) \\ $$$$\:\:\:\:\:\:\:\:\:\:{then}\:\:{evaluate}\:: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:{A}=\frac{{t}_{\mathrm{10}} −\mathrm{2}{t}_{\mathrm{8}} }{\mathrm{2}{t}_{\mathrm{9}} }\:=??? \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:...{m}.{n}.\mathrm{1970}... \\ $$

Question Number 120839 Answers: 3 Comments: 0

Question Number 120809 Answers: 0 Comments: 0

Find the largest number of positive integers that can be found in such a way that any two of them a and b ( a≠b) satisfy the next inequality ∣a−b∣≥((ab)/(100))

$$\mathrm{Find}\:\mathrm{the}\:\mathrm{largest}\:\mathrm{number}\:\mathrm{of}\:\mathrm{positive} \\ $$$$\mathrm{integers}\:\mathrm{that}\:\mathrm{can}\:\mathrm{be}\:\mathrm{found}\:\mathrm{in}\:\mathrm{such}\:\mathrm{a}\:\mathrm{way} \\ $$$$\mathrm{that}\:\mathrm{any}\:\mathrm{two}\:\mathrm{of}\:\mathrm{them}\:{a}\:\mathrm{and}\:{b}\:\left(\:{a}\neq{b}\right)\: \\ $$$$\mathrm{satisfy}\:\mathrm{the}\:\mathrm{next}\:\mathrm{inequality}\:\mid{a}−{b}\mid\geqslant\frac{{ab}}{\mathrm{100}} \\ $$

Question Number 120780 Answers: 2 Comments: 2

solve x^2^x =−(1/2)

$${solve}\:{x}^{\mathrm{2}^{{x}} } =−\frac{\mathrm{1}}{\mathrm{2}} \\ $$

Question Number 120711 Answers: 3 Comments: 0

show that 1+2+3+4...=((−1)/8)

$${show}\:{that}\:\mathrm{1}+\mathrm{2}+\mathrm{3}+\mathrm{4}...=\frac{−\mathrm{1}}{\mathrm{8}} \\ $$

Question Number 120636 Answers: 0 Comments: 23

selective Binomial

$${selective}\:{Binomial} \\ $$

Question Number 120601 Answers: 1 Comments: 0

Find the range of values of x for which the expansion of the binomial (2 − 3x)^(−4) is valid. I need help with explanation please