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AlgebraQuestion and Answers: Page 62

Question Number 199159 Answers: 1 Comments: 0

((8(x+1)))^(1/4) +(((x+1)/(x−1)))^(1/4) =((5(x^2 +1)^2 −3))^(1/4) x=?

$$\:\sqrt[{\mathrm{4}}]{\mathrm{8}\left(\mathrm{x}+\mathrm{1}\right)}\:+\sqrt[{\mathrm{4}}]{\frac{\mathrm{x}+\mathrm{1}}{\mathrm{x}−\mathrm{1}}}\:=\sqrt[{\mathrm{4}}]{\mathrm{5}\left(\mathrm{x}^{\mathrm{2}} +\mathrm{1}\right)^{\mathrm{2}} −\mathrm{3}}\: \\ $$$$\:\mathrm{x}=? \\ $$

Question Number 199355 Answers: 1 Comments: 0

Question Number 199135 Answers: 7 Comments: 0

a + (1/a) = 3 find: a^5 + (1/a^5 ) = ?

$$\mathrm{a}\:+\:\frac{\mathrm{1}}{\mathrm{a}}\:=\:\mathrm{3} \\ $$$$\mathrm{find}:\:\:\:\mathrm{a}^{\mathrm{5}} \:+\:\frac{\mathrm{1}}{\mathrm{a}^{\mathrm{5}} }\:\:=\:\:? \\ $$

Question Number 199133 Answers: 1 Comments: 0

a^2 b − 1 = 1999 how many natural solutions of the equation (a,b) have?

$$\mathrm{a}^{\mathrm{2}} \mathrm{b}\:−\:\mathrm{1}\:=\:\mathrm{1999} \\ $$$$\mathrm{how}\:\mathrm{many}\:\mathrm{natural}\:\mathrm{solutions}\:\mathrm{of}\:\mathrm{the} \\ $$$$\mathrm{equation}\:\left(\mathrm{a},\mathrm{b}\right)\:\mathrm{have}? \\ $$

Question Number 199112 Answers: 2 Comments: 0

{ ((a^2 − b = 73)),((b^2 − a = 73)) :} find: a,b = ?

$$\begin{cases}{\mathrm{a}^{\mathrm{2}} \:−\:\mathrm{b}\:=\:\mathrm{73}}\\{\mathrm{b}^{\mathrm{2}} \:−\:\mathrm{a}\:=\:\mathrm{73}}\end{cases}\:\:\:\:\:\mathrm{find}:\:\mathrm{a},\mathrm{b}\:=\:? \\ $$

Question Number 199109 Answers: 2 Comments: 1

Q: α , β ,γ are the roots of the following equation . find the value of: Eq^( n) : x^( 3) −2x^2 + x + 2=0 E = (α/(β +γ)) +(β/(α +γ)) +(γ/(α+ β))

$$ \\ $$$$\:{Q}:\:\:\:\:\alpha\:,\:\beta\:,\gamma\:{are}\:{the}\:{roots}\:{of}\:{the}\:{following} \\ $$$$\:\:\:\:\:{equation}\:.\:{find}\:{the}\:{value}\:{of}: \\ $$$$ \\ $$$$\:\:\:\:\:{Eq}^{\:{n}} \::\:\:\:{x}^{\:\mathrm{3}} −\mathrm{2}{x}^{\mathrm{2}} \:+\:{x}\:+\:\mathrm{2}=\mathrm{0} \\ $$$$\:\:\:{E}\:=\:\frac{\alpha}{\beta\:+\gamma}\:+\frac{\beta}{\alpha\:+\gamma}\:+\frac{\gamma}{\alpha+\:\beta} \\ $$$$ \\ $$

Question Number 199093 Answers: 0 Comments: 0

Question Number 199033 Answers: 1 Comments: 3

Question Number 199015 Answers: 2 Comments: 0

Question Number 198968 Answers: 2 Comments: 0

Find the polynomial with roots that exceed the roots of f(x)=3x^3 −14x^2 +x+62=0 by 3. Hence determine the value of (1/(a+3))+(1/(b+3))+(1/(c+3)), where a,b and c are roots.

$${Find}\:{the}\:{polynomial}\:{with}\:{roots}\:{that} \\ $$$${exceed}\:{the}\:{roots}\:{of}\: \\ $$$${f}\left({x}\right)=\mathrm{3}{x}^{\mathrm{3}} −\mathrm{14}{x}^{\mathrm{2}} +{x}+\mathrm{62}=\mathrm{0}\:{by}\:\mathrm{3}.\:{Hence} \\ $$$${determine}\:{the}\:{value}\:{of}\:\frac{\mathrm{1}}{{a}+\mathrm{3}}+\frac{\mathrm{1}}{{b}+\mathrm{3}}+\frac{\mathrm{1}}{{c}+\mathrm{3}}, \\ $$$${where}\:{a},{b}\:{and}\:{c}\:{are}\:{roots}. \\ $$

Question Number 198954 Answers: 1 Comments: 0

Convert this decimal number to praction number 1. 0.3333... =... 2. 2.1111...=... 3. 0.1313....=...

$$\:\mathrm{Convert}\:\mathrm{this}\:\mathrm{decimal}\:\mathrm{number}\:\mathrm{to}\: \\ $$$$\:\:\mathrm{praction}\:\mathrm{number} \\ $$$$\mathrm{1}.\:\mathrm{0}.\mathrm{3333}...\:=... \\ $$$$\mathrm{2}.\:\:\mathrm{2}.\mathrm{1111}...=... \\ $$$$\mathrm{3}.\:\mathrm{0}.\mathrm{1313}....=... \\ $$

Question Number 198951 Answers: 0 Comments: 1

(√(8+(√(48)) ))=....?

$$\sqrt{\mathrm{8}+\sqrt{\mathrm{48}}\:}=....? \\ $$

Question Number 198932 Answers: 1 Comments: 0

Find the value of m given that the roots of x^4 −15x^3 +70x^2 −120x+m=0 form a geometric progression.

$${Find}\:{the}\:{value}\:{of}\:{m}\:{given}\:{that}\:{the} \\ $$$${roots}\:{of}\:{x}^{\mathrm{4}} −\mathrm{15}{x}^{\mathrm{3}} +\mathrm{70}{x}^{\mathrm{2}} −\mathrm{120}{x}+{m}=\mathrm{0} \\ $$$${form}\:{a}\:{geometric}\:{progression}. \\ $$

Question Number 198931 Answers: 2 Comments: 0

Find the value of t: t = (1/3)+(2/9)+(3/(27))+.......+(n/3^n )+.....

$${Find}\:{the}\:{value}\:{of}\:{t}:\: \\ $$$${t}\:=\:\frac{\mathrm{1}}{\mathrm{3}}+\frac{\mathrm{2}}{\mathrm{9}}+\frac{\mathrm{3}}{\mathrm{27}}+.......+\frac{{n}}{\mathrm{3}^{{n}} }+..... \\ $$

Question Number 198919 Answers: 1 Comments: 1

Find the sum of the fourth powers of the roots of equation: 7x^3 −21x^2 +9x+2=0

$${Find}\:{the}\:{sum}\:{of}\:{the}\:{fourth}\:{powers}\:{of} \\ $$$${the}\:{roots}\:{of}\:{equation}: \\ $$$$\mathrm{7}{x}^{\mathrm{3}} −\mathrm{21}{x}^{\mathrm{2}} +\mathrm{9}{x}+\mathrm{2}=\mathrm{0} \\ $$

Question Number 198903 Answers: 1 Comments: 1

Find the minimum value of (a/(b+c))+(b/(c+a))+(c/(a+b)) for all positive real numbers

$${Find}\:{the}\:{minimum}\:{value}\:{of}\: \\ $$$$\frac{{a}}{{b}+{c}}+\frac{{b}}{{c}+{a}}+\frac{{c}}{{a}+{b}}\:{for}\:{all}\:{positive}\:{real} \\ $$$${numbers} \\ $$

Question Number 198902 Answers: 2 Comments: 0

Given that k^2 −3k+5=0, determine the value of k^4 −6k^3 +9k^2 −7

$${Given}\:{that}\:{k}^{\mathrm{2}} −\mathrm{3}{k}+\mathrm{5}=\mathrm{0},\:{determine} \\ $$$${the}\:{value}\:{of}\:{k}^{\mathrm{4}} −\mathrm{6}{k}^{\mathrm{3}} +\mathrm{9}{k}^{\mathrm{2}} −\mathrm{7} \\ $$

Question Number 198850 Answers: 1 Comments: 0

p(x+1)+p(x−1)=4x^2 −2x+10 p(x)=?

$$ \\ $$$$\mathrm{p}\left(\mathrm{x}+\mathrm{1}\right)+\mathrm{p}\left(\mathrm{x}−\mathrm{1}\right)=\mathrm{4x}^{\mathrm{2}} −\mathrm{2x}+\mathrm{10} \\ $$$$\mathrm{p}\left(\mathrm{x}\right)=? \\ $$$$ \\ $$$$ \\ $$

Question Number 198814 Answers: 2 Comments: 0

Simplify: ((((√(x + 4 (√(x - 4)))) + (√(x - 4 (√(x - 4))))) (√(x - 8)))/(4 (√(x^2 - 12x + 32))))

$$\mathrm{Simplify}: \\ $$$$\frac{\left(\sqrt{\mathrm{x}\:+\:\mathrm{4}\:\sqrt{\mathrm{x}\:-\:\mathrm{4}}}\:+\:\sqrt{\mathrm{x}\:-\:\mathrm{4}\:\sqrt{\mathrm{x}\:-\:\mathrm{4}}}\right)\:\sqrt{\mathrm{x}\:-\:\mathrm{8}}}{\mathrm{4}\:\sqrt{\mathrm{x}^{\mathrm{2}} \:-\:\mathrm{12x}\:+\:\mathrm{32}}} \\ $$

Question Number 198813 Answers: 1 Comments: 0

suppose that : E= (√( 9 + 4 ( Σ_(k=2) ^n a_( k) ^( 2) ))) is given let a_( k) = a_(k−1) . (a_( k−1) +1) and a_1 =1 , a_( 2) = 2 , a_( 3) = 6 , a_4 = 42 , a_( 5) = 1806 and etc find the value of E =?

$$ \\ $$$$\:\:\:\:\:{suppose}\:\:{that}\:: \\ $$$$ \\ $$$$\:\:\:\:\:\:{E}=\:\sqrt{\:\mathrm{9}\:+\:\mathrm{4}\:\left(\:\underset{{k}=\mathrm{2}} {\overset{{n}} {\sum}}\:\:{a}_{\:{k}} ^{\:\mathrm{2}} \:\right)} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:{is}\:\:{given} \\ $$$$\:\:\:\:\:{let}\:\:\:\:{a}_{\:{k}} \:=\:{a}_{{k}−\mathrm{1}} \:.\:\left({a}_{\:{k}−\mathrm{1}} \:+\mathrm{1}\right) \\ $$$$\:\:\:\:\:{and}\:\:\:{a}_{\mathrm{1}} \:=\mathrm{1}\:,\:\:\:{a}_{\:\mathrm{2}} \:=\:\mathrm{2}\:\:,\:{a}_{\:\mathrm{3}} =\:\mathrm{6}\:, \\ $$$$\:\:\:\:\:\:{a}_{\mathrm{4}} \:=\:\:\mathrm{42}\:\:\:,\:{a}_{\:\mathrm{5}} \:=\:\mathrm{1806}\:\:\:\:{and}\:\:{etc} \\ $$$$\:\:\:{find}\:{the}\:\:{value}\:\:{of}\:\:\:\:{E}\:=? \\ $$

Question Number 199092 Answers: 5 Comments: 0

Let the polynomial p(x)=5x^3 +3x^2 −10 have roots a,b and c. What is the value of (a/(b+c))+(b/(c+a))+(c/(a+b))?

$${Let}\:{the}\:{polynomial}\:{p}\left({x}\right)=\mathrm{5}{x}^{\mathrm{3}} +\mathrm{3}{x}^{\mathrm{2}} −\mathrm{10} \\ $$$${have}\:{roots}\:{a},{b}\:{and}\:{c}.\:{What}\:{is}\:{the}\:{value} \\ $$$${of}\:\frac{{a}}{{b}+{c}}+\frac{{b}}{{c}+{a}}+\frac{{c}}{{a}+{b}}? \\ $$

Question Number 198772 Answers: 0 Comments: 1

x^4 +ax^3 +bx^2 +cx+d=0

$${x}^{\mathrm{4}} +{ax}^{\mathrm{3}} +{bx}^{\mathrm{2}} +{cx}+{d}=\mathrm{0} \\ $$

Question Number 198754 Answers: 1 Comments: 0

Question Number 198647 Answers: 3 Comments: 1

Question Number 198575 Answers: 1 Comments: 3

Question Number 198559 Answers: 0 Comments: 0

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