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Question Number 155400 Answers: 0 Comments: 1

x^2 +x+5xy+6y^2 +2y−2=0

$${x}^{\mathrm{2}} +{x}+\mathrm{5}{xy}+\mathrm{6}{y}^{\mathrm{2}} +\mathrm{2}{y}−\mathrm{2}=\mathrm{0} \\ $$

Question Number 155399 Answers: 2 Comments: 0

Question Number 155393 Answers: 1 Comments: 0

∣∣x−4∣−4∣ ≥ 4

$$\:\:\mid\mid\mathrm{x}−\mathrm{4}\mid−\mathrm{4}\mid\:\geqslant\:\mathrm{4}\: \\ $$

Question Number 155392 Answers: 0 Comments: 0

lim_(x→0) ((((a^(x+1) +b^(x+1) )^2 )/(a+b)))^(1/x) =…?

$$\:\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\left(\frac{\left({a}^{{x}+\mathrm{1}} +{b}^{{x}+\mathrm{1}} \right)^{\mathrm{2}} }{{a}+{b}}\right)^{\frac{\mathrm{1}}{{x}}} =\ldots? \\ $$

Question Number 155386 Answers: 1 Comments: 0

Prove that: Σ_(k=1) ^∞ (((H_k )^3 )/2^k ) = ((3ζ(3) + ln^3 2 + π^2 ln2)/3)

$$\mathrm{Prove}\:\mathrm{that}: \\ $$$$\underset{\boldsymbol{\mathrm{k}}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{\left(\mathrm{H}_{\boldsymbol{\mathrm{k}}} \right)^{\mathrm{3}} }{\mathrm{2}^{\boldsymbol{\mathrm{k}}} }\:=\:\frac{\mathrm{3}\zeta\left(\mathrm{3}\right)\:+\:\mathrm{ln}^{\mathrm{3}} \mathrm{2}\:+\:\pi^{\mathrm{2}} \mathrm{ln2}}{\mathrm{3}}\:\: \\ $$

Question Number 155384 Answers: 2 Comments: 1

Solve : x^2 − (5−i)x + (12−5i) = 0

$$\boldsymbol{{Solve}}\::\:\boldsymbol{{x}}^{\mathrm{2}} \:−\:\left(\mathrm{5}−\boldsymbol{{i}}\right)\boldsymbol{{x}}\:+\:\left(\mathrm{12}−\mathrm{5}\boldsymbol{{i}}\right)\:=\:\mathrm{0} \\ $$

Question Number 156093 Answers: 2 Comments: 0

Question Number 155382 Answers: 1 Comments: 0

Question Number 155381 Answers: 1 Comments: 5

Question Number 155377 Answers: 2 Comments: 0

For two non-negative real numbers: a^6 + b^6 = 2 Find a;b such that 3(a+b)=1+5(√(ab))

$$\mathrm{For}\:\mathrm{two}\:\mathrm{non}-\mathrm{negative}\:\mathrm{real}\:\mathrm{numbers}: \\ $$$$\mathrm{a}^{\mathrm{6}} \:+\:\mathrm{b}^{\mathrm{6}} \:=\:\mathrm{2} \\ $$$$\mathrm{Find}\:\:\mathrm{a};\mathrm{b}\:\:\mathrm{such}\:\mathrm{that}\:\:\mathrm{3}\left(\mathrm{a}+\mathrm{b}\right)=\mathrm{1}+\mathrm{5}\sqrt{\mathrm{ab}} \\ $$

Question Number 155372 Answers: 1 Comments: 4

Question Number 155365 Answers: 2 Comments: 0

y=((10)/((2x^2 +1)^5 )) find (dy/dx)

$$\:{y}=\frac{\mathrm{10}}{\left(\mathrm{2}{x}^{\mathrm{2}} +\mathrm{1}\right)^{\mathrm{5}} } \\ $$$$\:{find}\:\:\frac{{dy}}{{dx}} \\ $$

Question Number 155362 Answers: 0 Comments: 0

if a;b≥0 and a^4 + b^4 = 17 prove that: 15(a + b) ≥ 17 + 14(√(2ab))

$$\mathrm{if}\:\:\mathrm{a};\mathrm{b}\geqslant\mathrm{0}\:\:\mathrm{and}\:\:\mathrm{a}^{\mathrm{4}} \:+\:\mathrm{b}^{\mathrm{4}} \:=\:\mathrm{17}\:\:\mathrm{prove}\:\mathrm{that}: \\ $$$$\mathrm{15}\left(\mathrm{a}\:+\:\mathrm{b}\right)\:\geqslant\:\mathrm{17}\:+\:\mathrm{14}\sqrt{\mathrm{2ab}} \\ $$$$ \\ $$

Question Number 155361 Answers: 0 Comments: 0

x−4z+8y=7 8×+7z−y=4 x^2 +y^2 −z^2 =?

$${x}−\mathrm{4}{z}+\mathrm{8}{y}=\mathrm{7} \\ $$$$\mathrm{8}×+\mathrm{7}{z}−{y}=\mathrm{4} \\ $$$${x}^{\mathrm{2}} +{y}^{\mathrm{2}} −{z}^{\mathrm{2}} =? \\ $$

Question Number 155360 Answers: 1 Comments: 0

Question Number 155359 Answers: 0 Comments: 1

Question Number 155357 Answers: 1 Comments: 1

Question Number 155356 Answers: 0 Comments: 0

Find the coefficient of term “ a^m b^(2m) ” in (1+a)^m (1+b)^(n+m) (1+a+b)^m .

$$\mathrm{Find}\:\mathrm{the}\:\mathrm{coefficient}\:\mathrm{of}\:\mathrm{term}\:``\:\mathrm{a}^{\mathrm{m}} \mathrm{b}^{\mathrm{2m}} \:''\:\mathrm{in}\:\left(\mathrm{1}+\mathrm{a}\right)^{\mathrm{m}} \left(\mathrm{1}+\mathrm{b}\right)^{\mathrm{n}+\mathrm{m}} \left(\mathrm{1}+\mathrm{a}+\mathrm{b}\right)^{\mathrm{m}} . \\ $$

Question Number 155353 Answers: 2 Comments: 0

show that lim_(x→0) ((sinx)/x) = 1

$$\boldsymbol{{show}}\:\boldsymbol{{that}}\:\:\boldsymbol{{lim}}_{\boldsymbol{{x}}\rightarrow\mathrm{0}} \frac{\boldsymbol{{sinx}}}{\boldsymbol{{x}}}\:=\:\mathrm{1} \\ $$

Question Number 155352 Answers: 0 Comments: 0

Question Number 155345 Answers: 2 Comments: 1

Solve the equation in R ((5(√(x+1)))/( (√(1 - x + x^2 )) + 2(√(x + 1)))) = 4x^2 - 5x + 5

$$\mathrm{Solve}\:\mathrm{the}\:\mathrm{equation}\:\mathrm{in}\:\mathbb{R} \\ $$$$\frac{\mathrm{5}\sqrt{\mathrm{x}+\mathrm{1}}}{\:\sqrt{\mathrm{1}\:-\:\mathrm{x}\:+\:\mathrm{x}^{\mathrm{2}} }\:+\:\mathrm{2}\sqrt{\mathrm{x}\:+\:\mathrm{1}}}\:=\:\mathrm{4x}^{\mathrm{2}} \:-\:\mathrm{5x}\:+\:\mathrm{5} \\ $$

Question Number 155344 Answers: 1 Comments: 0

Solve for integers: x^2 - 3x(y^2 + y - 1) + 4y^2 + 4y - 6 = 0

$$\mathrm{Solve}\:\mathrm{for}\:\mathrm{integers}: \\ $$$$ \\ $$$$\mathrm{x}^{\mathrm{2}} \:-\:\mathrm{3x}\left(\mathrm{y}^{\mathrm{2}} \:+\:\mathrm{y}\:-\:\mathrm{1}\right)\:+\:\mathrm{4y}^{\mathrm{2}} \:+\:\mathrm{4y}\:-\:\mathrm{6}\:=\:\mathrm{0} \\ $$

Question Number 155335 Answers: 1 Comments: 0

2x^5 + 3x^4 - 7x^3 - 7x^2 + 3x + 2 = 0 x_(1.2.3.4.5) = ?

$$\mathrm{2x}^{\mathrm{5}} \:+\:\mathrm{3x}^{\mathrm{4}} \:-\:\mathrm{7x}^{\mathrm{3}} \:-\:\mathrm{7x}^{\mathrm{2}} \:+\:\mathrm{3x}\:+\:\mathrm{2}\:=\:\mathrm{0} \\ $$$$\mathrm{x}_{\mathrm{1}.\mathrm{2}.\mathrm{3}.\mathrm{4}.\mathrm{5}} \:=\:? \\ $$

Question Number 155331 Answers: 1 Comments: 0

what is limit? also where we use it.

$$\mathrm{what}\:\mathrm{is}\:\mathrm{limit}?\:\mathrm{also}\:\mathrm{where}\:\mathrm{we}\:\mathrm{use}\:\mathrm{it}. \\ $$

Question Number 155323 Answers: 0 Comments: 0

Question Number 155316 Answers: 4 Comments: 0

lim_(x→∞) ((√(x^2 +3x))−x)=?

$$\underset{{x}\rightarrow\infty} {\mathrm{lim}}\:\left(\sqrt{{x}^{\mathrm{2}} +\mathrm{3}{x}}−{x}\right)=? \\ $$

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