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AlgebraQuestion and Answers: Page 289

Question Number 77965    Answers: 1   Comments: 9

solve for x,y,z ∈N 35x+21y+60z=665

$${solve}\:{for}\:{x},{y},{z}\:\in\mathbb{N} \\ $$$$\mathrm{35}{x}+\mathrm{21}{y}+\mathrm{60}{z}=\mathrm{665} \\ $$

Question Number 77902    Answers: 0   Comments: 8

Question Number 77885    Answers: 2   Comments: 0

solve for : x 1.(√((x−a)(x−b)))+(√((x−b)(x−c)))+(√((x−c)(x−a)))=d [a,b,c,d∈R try for: a=4,b=3,c=2,d=1] 2. (x−a^2 )(√(x−a))+(x−a)(√(x−a^2 ))=a^2 +a+1 3. (x−a^2 )(√(x^2 −a))+(x^2 −a)(√(x−a^2 ))=a^2 +a+1 [a∈R try for: a=(1/2) ]

$$\boldsymbol{\mathrm{solve}}\:\boldsymbol{\mathrm{for}}\::\:\boldsymbol{\mathrm{x}} \\ $$$$\mathrm{1}.\sqrt{\left(\boldsymbol{\mathrm{x}}−\boldsymbol{\mathrm{a}}\right)\left(\boldsymbol{\mathrm{x}}−\boldsymbol{\mathrm{b}}\right)}+\sqrt{\left(\boldsymbol{\mathrm{x}}−\boldsymbol{\mathrm{b}}\right)\left(\boldsymbol{\mathrm{x}}−\boldsymbol{\mathrm{c}}\right)}+\sqrt{\left(\boldsymbol{\mathrm{x}}−\boldsymbol{\mathrm{c}}\right)\left(\boldsymbol{\mathrm{x}}−\boldsymbol{\mathrm{a}}\right)}=\boldsymbol{\mathrm{d}} \\ $$$$\left[\boldsymbol{\mathrm{a}},\boldsymbol{\mathrm{b}},\boldsymbol{\mathrm{c}},\boldsymbol{\mathrm{d}}\in\boldsymbol{\mathrm{R}}\right. \\ $$$$\left.\mathrm{try}\:\mathrm{for}:\:\:\mathrm{a}=\mathrm{4},\mathrm{b}=\mathrm{3},\mathrm{c}=\mathrm{2},\mathrm{d}=\mathrm{1}\right] \\ $$$$\mathrm{2}.\:\left(\boldsymbol{\mathrm{x}}−\boldsymbol{\mathrm{a}}^{\mathrm{2}} \right)\sqrt{\boldsymbol{\mathrm{x}}−\boldsymbol{\mathrm{a}}}+\left(\boldsymbol{\mathrm{x}}−\boldsymbol{\mathrm{a}}\right)\sqrt{\boldsymbol{\mathrm{x}}−\boldsymbol{\mathrm{a}}^{\mathrm{2}} }=\boldsymbol{\mathrm{a}}^{\mathrm{2}} +\boldsymbol{\mathrm{a}}+\mathrm{1} \\ $$$$\mathrm{3}.\:\left(\boldsymbol{\mathrm{x}}−\boldsymbol{\mathrm{a}}^{\mathrm{2}} \right)\sqrt{\boldsymbol{\mathrm{x}}^{\mathrm{2}} −\boldsymbol{\mathrm{a}}}+\left(\boldsymbol{\mathrm{x}}^{\mathrm{2}} −\boldsymbol{\mathrm{a}}\right)\sqrt{\boldsymbol{\mathrm{x}}−\boldsymbol{\mathrm{a}}^{\mathrm{2}} }=\boldsymbol{\mathrm{a}}^{\mathrm{2}} +\boldsymbol{\mathrm{a}}+\mathrm{1} \\ $$$$\left[\boldsymbol{\mathrm{a}}\in\boldsymbol{\mathrm{R}}\right. \\ $$$$\left.\mathrm{try}\:\mathrm{for}:\:\mathrm{a}=\frac{\mathrm{1}}{\mathrm{2}}\:\right] \\ $$$$ \\ $$

Question Number 77883    Answers: 1   Comments: 7

Question Number 77881    Answers: 0   Comments: 5

Question Number 77864    Answers: 1   Comments: 1

Question Number 77855    Answers: 0   Comments: 0

Question Number 77819    Answers: 2   Comments: 0

Question Number 77804    Answers: 0   Comments: 2

Question Number 77800    Answers: 0   Comments: 0

if a_1 =1, a_2 =3 and a_n =(√(a_(n−1) +a_(n−2) )) with n≥3 find a_n in explicit form.

$${if}\:{a}_{\mathrm{1}} =\mathrm{1},\:{a}_{\mathrm{2}} =\mathrm{3}\:{and} \\ $$$${a}_{{n}} =\sqrt{{a}_{{n}−\mathrm{1}} +{a}_{{n}−\mathrm{2}} }\:{with}\:{n}\geqslant\mathrm{3} \\ $$$${find}\:{a}_{{n}} \:{in}\:{explicit}\:{form}. \\ $$

Question Number 77799    Answers: 1   Comments: 0

if a_1 =3 and a_(n+1) =3a_n +6n^2 −12n+2 find a_n in terms of n.

$${if}\:{a}_{\mathrm{1}} =\mathrm{3}\:{and} \\ $$$${a}_{{n}+\mathrm{1}} =\mathrm{3}{a}_{{n}} +\mathrm{6}{n}^{\mathrm{2}} −\mathrm{12}{n}+\mathrm{2} \\ $$$${find}\:{a}_{{n}} \:{in}\:{terms}\:{of}\:{n}. \\ $$

Question Number 77741    Answers: 1   Comments: 1

Question Number 77725    Answers: 2   Comments: 4

Question Number 77721    Answers: 0   Comments: 1

Question Number 77604    Answers: 2   Comments: 0

given (((a−b)(b−c)(c−a))/((a+b)(b+c)(c+a)))=−(1/(30)) what the value of (b/(a+b))+(c/(b+c))+(a/(c+a)) ?

$${given} \\ $$$$\frac{\left({a}−{b}\right)\left({b}−{c}\right)\left({c}−{a}\right)}{\left({a}+{b}\right)\left({b}+{c}\right)\left({c}+{a}\right)}=−\frac{\mathrm{1}}{\mathrm{30}} \\ $$$${what}\:{the}\:{value}\:{of}\: \\ $$$$\frac{{b}}{{a}+{b}}+\frac{{c}}{{b}+{c}}+\frac{{a}}{{c}+{a}}\:? \\ $$

Question Number 77556    Answers: 0   Comments: 2

1. 1×1!×2!+2×2!×3!+3×3!×4!+....=? 2. ((1+(√2))/(2+(√3)))+((2+(√3))/(3+(√4)))+((3+(√4))/(4+(√5)))+......=? 3. (1/(1+(√2)+(√3)))+(2/((√2)+(√3)+(√4)))+(3/((√3)+(√4)+(√5)))+....=?

$$\mathrm{1}.\:\:\:\mathrm{1}×\mathrm{1}!×\mathrm{2}!+\mathrm{2}×\mathrm{2}!×\mathrm{3}!+\mathrm{3}×\mathrm{3}!×\mathrm{4}!+....=? \\ $$$$\mathrm{2}.\:\:\:\:\frac{\mathrm{1}+\sqrt{\mathrm{2}}}{\mathrm{2}+\sqrt{\mathrm{3}}}+\frac{\mathrm{2}+\sqrt{\mathrm{3}}}{\mathrm{3}+\sqrt{\mathrm{4}}}+\frac{\mathrm{3}+\sqrt{\mathrm{4}}}{\mathrm{4}+\sqrt{\mathrm{5}}}+......=? \\ $$$$\mathrm{3}.\:\:\:\frac{\mathrm{1}}{\mathrm{1}+\sqrt{\mathrm{2}}+\sqrt{\mathrm{3}}}+\frac{\mathrm{2}}{\sqrt{\mathrm{2}}+\sqrt{\mathrm{3}}+\sqrt{\mathrm{4}}}+\frac{\mathrm{3}}{\sqrt{\mathrm{3}}+\sqrt{\mathrm{4}}+\sqrt{\mathrm{5}}}+....=?\: \\ $$

Question Number 77524    Answers: 1   Comments: 2

Question Number 77513    Answers: 0   Comments: 3

Question Number 77506    Answers: 1   Comments: 2

Question Number 77462    Answers: 0   Comments: 0

Question Number 77459    Answers: 1   Comments: 0

the greatest value of n so that only one value of k satisfies (8/(15))<(n/(n+k))<(7/(13)) is

$$ \\ $$$$ \\ $$$${the}\:{greatest}\:{value}\:{of}\:{n}\:{so}\:{that}\: \\ $$$${only}\:{one}\:{value}\:{of}\:{k}\:{satisfies}\: \\ $$$$\frac{\mathrm{8}}{\mathrm{15}}<\frac{{n}}{{n}+{k}}<\frac{\mathrm{7}}{\mathrm{13}}\:{is}\: \\ $$

Question Number 77451    Answers: 1   Comments: 1

Question Number 77412    Answers: 0   Comments: 7

Question Number 77379    Answers: 0   Comments: 0

Question Number 77377    Answers: 0   Comments: 0

Question Number 77346    Answers: 0   Comments: 3

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