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AlgebraQuestion and Answers: Page 287

Question Number 76167 Answers: 3 Comments: 0

Question Number 76153 Answers: 0 Comments: 0

Question Number 76127 Answers: 0 Comments: 0

Question Number 76126 Answers: 1 Comments: 9

Question Number 76122 Answers: 4 Comments: 0

Question Number 76061 Answers: 1 Comments: 0

What′s the minimum value of ((13a+13b+2c)/(2a+2b))+((24a−b+13c)/(2b+2c))+((−a+24b+13c)/(2a+2c))? (a,b,c are positive numbers.) I think nobody can solve this.

$$\mathrm{What}'\mathrm{s}\:\mathrm{the}\:\mathrm{minimum}\:\mathrm{value}\:\mathrm{of} \\ $$$$\frac{\mathrm{13}{a}+\mathrm{13}{b}+\mathrm{2}{c}}{\mathrm{2}{a}+\mathrm{2}{b}}+\frac{\mathrm{24}{a}−{b}+\mathrm{13}{c}}{\mathrm{2}{b}+\mathrm{2}{c}}+\frac{−{a}+\mathrm{24}{b}+\mathrm{13}{c}}{\mathrm{2}{a}+\mathrm{2}{c}}? \\ $$$$\left({a},{b},{c}\:\mathrm{are}\:\mathrm{positive}\:\mathrm{numbers}.\right) \\ $$$$\mathrm{I}\:\mathrm{think}\:\mathrm{nobody}\:\mathrm{can}\:\mathrm{solve}\:\mathrm{this}. \\ $$

Question Number 76048 Answers: 2 Comments: 0

∫e^x^2 dx

$$\int{e}^{{x}^{\mathrm{2}} } {dx} \\ $$

Question Number 76009 Answers: 1 Comments: 0

hiw do i solve 2^x = 4x?

$${hiw}\:{do}\:{i}\:{solve} \\ $$$$\mathrm{2}^{{x}} \:=\:\mathrm{4}{x}? \\ $$

Question Number 76003 Answers: 1 Comments: 0

22+2

$$\mathrm{22}+\mathrm{2} \\ $$

Question Number 75990 Answers: 0 Comments: 0

Question Number 75985 Answers: 1 Comments: 0

Question Number 75933 Answers: 0 Comments: 2

solve the inequality a. ln(2x−e) >1 b. (lnx)^2 −lnx−6<0 c. ∣x∣ + ∣x+2∣ ≥ 2 d. ∣2x−5∣ + ∣x +2∣ > 7

$${solve}\:{the}\:{inequality} \\ $$$${a}.\:\:{ln}\left(\mathrm{2}{x}−{e}\right)\:>\mathrm{1} \\ $$$${b}.\:\left({lnx}\right)^{\mathrm{2}} −{lnx}−\mathrm{6}<\mathrm{0} \\ $$$${c}.\:\mid{x}\mid\:+\:\mid{x}+\mathrm{2}\mid\:\geqslant\:\mathrm{2} \\ $$$${d}.\:\mid\mathrm{2}{x}−\mathrm{5}\mid\:+\:\mid{x}\:+\mathrm{2}\mid\:>\:\mathrm{7} \\ $$

Question Number 75932 Answers: 1 Comments: 1

solve for x the following a. ∣x∣ + 3x −4 =0 b. ∣x∣−1 = 0 c. x^2 +3∣x∣ +2 =0

$${solve}\:{for}\:{x}\:{the}\:{following} \\ $$$${a}.\:\mid{x}\mid\:+\:\mathrm{3}{x}\:−\mathrm{4}\:=\mathrm{0} \\ $$$${b}.\:\:\mid{x}\mid−\mathrm{1}\:=\:\mathrm{0} \\ $$$${c}.\:{x}^{\mathrm{2}} +\mathrm{3}\mid{x}\mid\:+\mathrm{2}\:=\mathrm{0} \\ $$$$ \\ $$

Question Number 75916 Answers: 0 Comments: 1

x^3 +x^2 −24x+36=0 prove that x=2,3,−6.

$${x}^{\mathrm{3}} +{x}^{\mathrm{2}} −\mathrm{24}{x}+\mathrm{36}=\mathrm{0} \\ $$$${prove}\:{that}\:{x}=\mathrm{2},\mathrm{3},−\mathrm{6}. \\ $$

Question Number 75913 Answers: 0 Comments: 1

x^3 −7x+6=0 prove that x=2,−3,1 .

$${x}^{\mathrm{3}} −\mathrm{7}{x}+\mathrm{6}=\mathrm{0} \\ $$$${prove}\:{that}\:{x}=\mathrm{2},−\mathrm{3},\mathrm{1}\:. \\ $$

Question Number 75918 Answers: 1 Comments: 0

Question Number 75883 Answers: 0 Comments: 2

If a^4 + b^4 + c^4 + d^4 = 16 Prove that, a^5 + b^5 + c^5 + d^5 ≤ 32

$$\mathrm{If}\:\:\:\:\mathrm{a}^{\mathrm{4}} \:+\:\mathrm{b}^{\mathrm{4}} \:+\:\mathrm{c}^{\mathrm{4}} \:+\:\mathrm{d}^{\mathrm{4}} \:\:\:=\:\:\:\mathrm{16} \\ $$$$\mathrm{Prove}\:\mathrm{that},\:\:\:\:\:\:\:\:\mathrm{a}^{\mathrm{5}} \:+\:\mathrm{b}^{\mathrm{5}} \:+\:\mathrm{c}^{\mathrm{5}} \:+\:\mathrm{d}^{\mathrm{5}} \:\:\:\leqslant\:\:\:\mathrm{32} \\ $$

Question Number 75845 Answers: 1 Comments: 2

{ ((x+yz=x^2 )),((y+xz=y^2 )),((z+xy=z^2 )) :} solve for x,y,z.

$$\begin{cases}{\boldsymbol{\mathrm{x}}+\boldsymbol{\mathrm{yz}}=\boldsymbol{\mathrm{x}}^{\mathrm{2}} }\\{\boldsymbol{\mathrm{y}}+\boldsymbol{\mathrm{xz}}=\boldsymbol{\mathrm{y}}^{\mathrm{2}} }\\{\boldsymbol{\mathrm{z}}+\boldsymbol{\mathrm{xy}}=\boldsymbol{\mathrm{z}}^{\mathrm{2}} }\end{cases}\:\:\:\:\:\boldsymbol{\mathrm{solve}}\:\boldsymbol{\mathrm{for}}\:\boldsymbol{\mathrm{x}},\boldsymbol{\mathrm{y}},\boldsymbol{\mathrm{z}}. \\ $$

Question Number 75828 Answers: 1 Comments: 1

Σ_(n=1) ^∞ (1/(10^n ))

$$\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{\mathrm{1}}{\mathrm{10}^{{n}} } \\ $$

Question Number 75846 Answers: 2 Comments: 0

sin^5 x+(√2)sinx=1 , x∈[0,2𝛑]

$$\boldsymbol{\mathrm{sin}}^{\mathrm{5}} \boldsymbol{\mathrm{x}}+\sqrt{\mathrm{2}}\boldsymbol{\mathrm{sinx}}=\mathrm{1}\:\:\:\:\:\:\:\:,\:\:\boldsymbol{\mathrm{x}}\in\left[\mathrm{0},\mathrm{2}\boldsymbol{\pi}\right] \\ $$

Question Number 75778 Answers: 1 Comments: 0

if x^2 +y^2 =p, x^3 +y^3 =q, find x^n +y^n in terms of p, q and n. (n≥4)

$${if}\:{x}^{\mathrm{2}} +{y}^{\mathrm{2}} ={p},\:{x}^{\mathrm{3}} +{y}^{\mathrm{3}} ={q}, \\ $$$${find}\:{x}^{{n}} +{y}^{{n}} \:{in}\:{terms}\:{of}\:{p},\:{q}\:{and}\:{n}. \\ $$$$\left({n}\geqslant\mathrm{4}\right) \\ $$

Question Number 75756 Answers: 0 Comments: 1

Σ_(x=1) ^(99) ((1/(2x+1)))

$$\underset{{x}=\mathrm{1}} {\overset{\mathrm{99}} {\sum}}\left(\frac{\mathrm{1}}{\mathrm{2}{x}+\mathrm{1}}\right) \\ $$

Question Number 75753 Answers: 1 Comments: 0

((((x^(1/3) +x^(−1/3) )^2 −2)/((x^(1/3) +x^(−1/3) )^2 +2))−x)^(3/4)

$$\left(\frac{\left(\mathrm{x}^{\mathrm{1}/\mathrm{3}} +\mathrm{x}^{−\mathrm{1}/\mathrm{3}} \right)^{\mathrm{2}} −\mathrm{2}}{\left(\mathrm{x}^{\mathrm{1}/\mathrm{3}} +\mathrm{x}^{−\mathrm{1}/\mathrm{3}} \right)^{\mathrm{2}} +\mathrm{2}}−\mathrm{x}\right)^{\mathrm{3}/\mathrm{4}} \\ $$

Question Number 75751 Answers: 0 Comments: 0

Question Number 75739 Answers: 1 Comments: 1

Question Number 75681 Answers: 1 Comments: 8

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