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AlgebraQuestion and Answers: Page 253

Question Number 102927    Answers: 3   Comments: 1

If (x/(x^2 + x + 1)) = (1/4) Find x + (1/x)

$$\mathrm{If}\:\:\:\frac{\mathrm{x}}{\mathrm{x}^{\mathrm{2}} \:\:+\:\:\mathrm{x}\:\:+\:\:\mathrm{1}}\:\:\:=\:\:\frac{\mathrm{1}}{\mathrm{4}} \\ $$$$\mathrm{Find}\:\:\:\:\:\mathrm{x}\:\:+\:\:\frac{\mathrm{1}}{\mathrm{x}} \\ $$

Question Number 102548    Answers: 0   Comments: 0

if n is a real number,find the least possible number of n,if n^2 −3n+(√(n−3)) −(√(n+3))

$${if}\:{n}\:{is}\:{a}\:{real}\:{number},{find}\:{the}\:{least}\:{possible}\:{number}\:{of}\:{n},{if} \\ $$$${n}^{\mathrm{2}} −\mathrm{3}{n}+\sqrt{{n}−\mathrm{3}}\:−\sqrt{{n}+\mathrm{3}} \\ $$

Question Number 102490    Answers: 1   Comments: 0

x^3 −bx−c=0 ; b, c >0 ; ((b/3))^3 >((c/2))^2 To find the three real roots without the use of trigonometric solution to cubic polynomial...

$${x}^{\mathrm{3}} −{bx}−{c}=\mathrm{0}\:\:\:\:\:;\:\:{b},\:{c}\:>\mathrm{0}\:;\:\:\left(\frac{{b}}{\mathrm{3}}\right)^{\mathrm{3}} >\left(\frac{{c}}{\mathrm{2}}\right)^{\mathrm{2}} \\ $$$${To}\:{find}\:{the}\:{three}\:{real}\:{roots}\:{without} \\ $$$${the}\:{use}\:{of}\:{trigonometric}\:{solution} \\ $$$${to}\:{cubic}\:{polynomial}... \\ $$

Question Number 102418    Answers: 1   Comments: 0

Question Number 102278    Answers: 3   Comments: 4

Find the greatest coefficient in the following without actually expand. (i) (5 − 3x)^(10) (ii) (5 + 3x)^(− 10)

$$\mathrm{Find}\:\mathrm{the}\:\mathrm{greatest}\:\mathrm{coefficient}\:\mathrm{in}\:\mathrm{the}\:\mathrm{following}\:\mathrm{without} \\ $$$$\mathrm{actually}\:\mathrm{expand}. \\ $$$$\left(\mathrm{i}\right)\:\:\:\:\:\:\:\:\left(\mathrm{5}\:\:−\:\:\mathrm{3x}\right)^{\mathrm{10}} \\ $$$$\left(\mathrm{ii}\right)\:\:\:\:\:\:\:\:\left(\mathrm{5}\:\:+\:\:\mathrm{3x}\right)^{−\:\mathrm{10}} \\ $$

Question Number 102201    Answers: 0   Comments: 0

Question Number 102186    Answers: 0   Comments: 0

Question Number 102179    Answers: 1   Comments: 0

Question Number 102178    Answers: 1   Comments: 0

Question Number 102109    Answers: 0   Comments: 0

Question Number 102078    Answers: 5   Comments: 0

Question Number 102002    Answers: 0   Comments: 6

Question Number 101971    Answers: 0   Comments: 2

Question Number 101961    Answers: 0   Comments: 4

Question Number 101951    Answers: 0   Comments: 3

Question Number 101921    Answers: 1   Comments: 1

Please, help i cannot solve problems such as: x^4 =1, x^5 =1, or x^n =1 n∈N...

$$\boldsymbol{{Please}},\:\boldsymbol{{help}}\:\:\boldsymbol{{i}}\:\:\boldsymbol{{cannot}}\:\boldsymbol{{solve}}\:\boldsymbol{{problems}} \\ $$$$\boldsymbol{{such}}\:\boldsymbol{{as}}:\:\boldsymbol{{x}}^{\mathrm{4}} =\mathrm{1},\:\boldsymbol{{x}}^{\mathrm{5}} =\mathrm{1},\:\boldsymbol{{or}}\:\boldsymbol{{x}}^{\boldsymbol{{n}}} =\mathrm{1}\:\boldsymbol{{n}}\in\mathbb{N}... \\ $$

Question Number 101803    Answers: 1   Comments: 2

((√2)−1)^x +((√2)+1)^x =((√6))^x

$$\left(\sqrt{\mathrm{2}}−\mathrm{1}\right)^{{x}} +\left(\sqrt{\mathrm{2}}+\mathrm{1}\right)^{{x}} =\left(\sqrt{\mathrm{6}}\right)^{{x}} \\ $$

Question Number 101800    Answers: 1   Comments: 3

Question Number 101742    Answers: 3   Comments: 0

{ ((ab+a+b = 5)),((bc + b+c = 14)),((ac + a+c = 9)) :} find a+b+c = ___

$$\begin{cases}{{ab}+{a}+{b}\:=\:\mathrm{5}}\\{{bc}\:+\:{b}+{c}\:=\:\mathrm{14}}\\{{ac}\:+\:{a}+{c}\:=\:\mathrm{9}}\end{cases} \\ $$$$\mathrm{find}\:{a}+{b}+{c}\:=\:\_\_\_ \\ $$

Question Number 101693    Answers: 3   Comments: 2

There are 4 identical mathematics books, 2 identic physics books and 2 identical chemistry books . How many ways to compile the eight books on the condition of the same book are not mutually adjacent?

$$\mathrm{There}\:\mathrm{are}\:\mathrm{4}\:\mathrm{identical}\:\mathrm{mathematics} \\ $$$$\mathrm{books},\:\mathrm{2}\:\mathrm{identic}\:\mathrm{physics}\:\mathrm{books} \\ $$$$\mathrm{and}\:\mathrm{2}\:\mathrm{identical}\:\mathrm{chemistry}\:\mathrm{books} \\ $$$$.\:\mathrm{How}\:\mathrm{many}\:\mathrm{ways}\:\mathrm{to}\:\mathrm{compile}\: \\ $$$$\mathrm{the}\:\mathrm{eight}\:\mathrm{books}\:\mathrm{on}\:\mathrm{the}\:\mathrm{condition} \\ $$$$\mathrm{of}\:\mathrm{the}\:\mathrm{same}\:\mathrm{book}\:\mathrm{are}\:\mathrm{not}\:\mathrm{mutually} \\ $$$$\mathrm{adjacent}? \\ $$

Question Number 105306    Answers: 1   Comments: 1

(1/(2+(√2))) +(1/(3(√2)+2(√3) ))+(1/(4(√3)+3(√4)))+...+(1/(100(√(99))+99(√(100))))

$$\frac{\mathrm{1}}{\mathrm{2}+\sqrt{\mathrm{2}}}\:+\frac{\mathrm{1}}{\mathrm{3}\sqrt{\mathrm{2}}+\mathrm{2}\sqrt{\mathrm{3}}\:}+\frac{\mathrm{1}}{\mathrm{4}\sqrt{\mathrm{3}}+\mathrm{3}\sqrt{\mathrm{4}}}+...+\frac{\mathrm{1}}{\mathrm{100}\sqrt{\mathrm{99}}+\mathrm{99}\sqrt{\mathrm{100}}} \\ $$

Question Number 101607    Answers: 0   Comments: 0

f(x)=(√(2x+7))+log_3 x f^(−1) (x)=?

$$\mathrm{f}\left(\mathrm{x}\right)=\sqrt{\mathrm{2x}+\mathrm{7}}+\mathrm{log}_{\mathrm{3}} \mathrm{x} \\ $$$$\mathrm{f}^{−\mathrm{1}} \left(\mathrm{x}\right)=?\:\:\:\:\:\: \\ $$

Question Number 101871    Answers: 1   Comments: 0

if a_1 = −4 , a_2 =−1 and a_n = a_(n+1) +a_(n+3 ) . find a_4 −a_1 ?

$${if}\:{a}_{\mathrm{1}} =\:−\mathrm{4}\:,\:{a}_{\mathrm{2}} =−\mathrm{1}\:{and}\: \\ $$$${a}_{{n}} \:=\:{a}_{{n}+\mathrm{1}} +{a}_{{n}+\mathrm{3}\:} .\:{find}\: \\ $$$${a}_{\mathrm{4}} −{a}_{\mathrm{1}} ? \\ $$

Question Number 101568    Answers: 1   Comments: 0

Question Number 101563    Answers: 2   Comments: 0

Question Number 105345    Answers: 1   Comments: 0

If the point ((√2) ,p) and (−(√2),q) lie on the graph y=x^3 +ax^2 +bx+c and q−p = 3 , then what the value of b ?

$${If}\:{the}\:{point}\:\left(\sqrt{\mathrm{2}}\:,{p}\right)\:{and}\:\left(−\sqrt{\mathrm{2}},{q}\right) \\ $$$${lie}\:{on}\:{the}\:{graph}\:{y}={x}^{\mathrm{3}} +{ax}^{\mathrm{2}} +{bx}+{c} \\ $$$${and}\:{q}−{p}\:=\:\mathrm{3}\:,\:{then}\:{what}\:{the} \\ $$$${value}\:{of}\:{b}\:?\: \\ $$

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