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AlgebraQuestion and Answers: Page 4

Question Number 223400    Answers: 1   Comments: 0

f(1)=2025 𝚺_1 ^n f(k)=n^2 .f(n) f(2025)=?

$$\boldsymbol{{f}}\left(\mathrm{1}\right)=\mathrm{2025} \\ $$$$\underset{\mathrm{1}} {\overset{\boldsymbol{{n}}} {\boldsymbol{\sum}}{f}}\left(\boldsymbol{{k}}\right)=\boldsymbol{{n}}^{\mathrm{2}} .\boldsymbol{{f}}\left(\boldsymbol{{n}}\right) \\ $$$$\boldsymbol{{f}}\left(\mathrm{2025}\right)=? \\ $$

Question Number 223354    Answers: 0   Comments: 6

Question Number 223267    Answers: 3   Comments: 0

r,s,t ; are the roots of: x^3 +5x+1=0 find: (r^3 βˆ’1)(s^3 βˆ’1)(t^3 βˆ’1)

$$\boldsymbol{{r}},\boldsymbol{{s}},\boldsymbol{{t}}\:;\:\boldsymbol{{are}}\:\boldsymbol{{the}}\:\boldsymbol{{roots}}\:\boldsymbol{{of}}: \\ $$$$\:\:\:\:\:\:\:\:\boldsymbol{{x}}^{\mathrm{3}} +\mathrm{5}\boldsymbol{{x}}+\mathrm{1}=\mathrm{0} \\ $$$$\boldsymbol{{find}}: \\ $$$$\:\:\:\:\:\:\left(\boldsymbol{{r}}^{\mathrm{3}} βˆ’\mathrm{1}\right)\left(\boldsymbol{{s}}^{\mathrm{3}} βˆ’\mathrm{1}\right)\left(\boldsymbol{{t}}^{\mathrm{3}} βˆ’\mathrm{1}\right) \\ $$

Question Number 223261    Answers: 0   Comments: 1

Question Number 223240    Answers: 1   Comments: 0

x^x =i number of solutions??

$${x}^{{x}} ={i} \\ $$$${number}\:{of}\:{solutions}?? \\ $$

Question Number 223230    Answers: 3   Comments: 0

Maksimum (((x^2 βˆ’ 4x + 1)/(x^2 + 1))) = ?

$$\mathrm{Maksimum}\:\left(\frac{\mathrm{x}^{\mathrm{2}} \:βˆ’\:\mathrm{4x}\:+\:\mathrm{1}}{\mathrm{x}^{\mathrm{2}} \:+\:\mathrm{1}}\right)\:=\:? \\ $$

Question Number 223216    Answers: 2   Comments: 0

Question Number 223203    Answers: 2   Comments: 0

Find x and y ix+y=ix^3 βˆ’y^3 and xy(yβˆ’ix)=c

$${Find}\:{x}\:{and}\:{y} \\ $$$$\:\:\:\:{ix}+{y}={ix}^{\mathrm{3}} βˆ’{y}^{\mathrm{3}} \\ $$$$\:\:\:{and}\: \\ $$$$\:\:\:\:{xy}\left({y}βˆ’{ix}\right)={c} \\ $$

Question Number 223189    Answers: 1   Comments: 3

(xβˆ’1)(x^2 βˆ’2)(x^3 βˆ’3)(x^4 βˆ’4)=36 x=?

$$\left(\boldsymbol{{x}}βˆ’\mathrm{1}\right)\left(\boldsymbol{{x}}^{\mathrm{2}} βˆ’\mathrm{2}\right)\left(\boldsymbol{{x}}^{\mathrm{3}} βˆ’\mathrm{3}\right)\left(\boldsymbol{{x}}^{\mathrm{4}} βˆ’\mathrm{4}\right)=\mathrm{36} \\ $$$$\boldsymbol{{x}}=? \\ $$

Question Number 223179    Answers: 1   Comments: 1

If: xy = e^(𝛑/4) Find: tg (ln ((x^3 /y))) βˆ™ tg (ln ((y^3 /x))) = ?

$$\mathrm{If}:\:\:\:\mathrm{xy}\:=\:\boldsymbol{\mathrm{e}}^{\frac{\boldsymbol{\pi}}{\mathrm{4}}} \\ $$$$\mathrm{Find}:\:\:\:\mathrm{tg}\:\left(\mathrm{ln}\:\left(\frac{\mathrm{x}^{\mathrm{3}} }{\mathrm{y}}\right)\right)\:\centerdot\:\mathrm{tg}\:\left(\mathrm{ln}\:\left(\frac{\mathrm{y}^{\mathrm{3}} }{\mathrm{x}}\right)\right)\:=\:? \\ $$

Question Number 223161    Answers: 2   Comments: 4

Solve for x if (√(x+1))+(√(xβˆ’1))=1

$${Solve}\:{for}\:{x}\:{if} \\ $$$$\:\sqrt{{x}+\mathrm{1}}+\sqrt{{x}βˆ’\mathrm{1}}=\mathrm{1} \\ $$

Question Number 223110    Answers: 1   Comments: 0

Question Number 223044    Answers: 0   Comments: 1

Question Number 222889    Answers: 1   Comments: 10

Question Number 222885    Answers: 3   Comments: 0

Question Number 222856    Answers: 1   Comments: 0

find the possible root of x^3 βˆ’2x^2 βˆ’5x+6=0 using the fixed point iteration method?

$$\boldsymbol{{find}}\:\boldsymbol{{the}}\:\boldsymbol{{possible}}\:\boldsymbol{{root}}\:\boldsymbol{{of}}\:\boldsymbol{{x}}^{\mathrm{3}} βˆ’\mathrm{2}\boldsymbol{{x}}^{\mathrm{2}} βˆ’\mathrm{5}\boldsymbol{{x}}+\mathrm{6}=\mathrm{0} \\ $$$$\boldsymbol{{using}}\:\boldsymbol{{the}}\:\boldsymbol{{fixed}}\:\boldsymbol{{point}}\:\boldsymbol{{iteration}}\:\boldsymbol{{method}}? \\ $$

Question Number 222847    Answers: 1   Comments: 0

let f(x)=1.013x^5 βˆ’5.262x^3 βˆ’0.01732x^2 +0.8389x βˆ’1.912. Evaluate f(2.279) by first calculating (2.279)^2 ,(2.279)^3 ,(2.279)^4 and(2.279)^5 using fourβˆ’digit round arithmetic. hence,compute the absolute and relative errors.

$$\boldsymbol{{let}}\:\boldsymbol{{f}}\left(\boldsymbol{{x}}\right)=\mathrm{1}.\mathrm{013}\boldsymbol{{x}}^{\mathrm{5}} βˆ’\mathrm{5}.\mathrm{262}\boldsymbol{{x}}^{\mathrm{3}} βˆ’\mathrm{0}.\mathrm{01732}\boldsymbol{{x}}^{\mathrm{2}} +\mathrm{0}.\mathrm{8389}\boldsymbol{{x}} \\ $$$$βˆ’\mathrm{1}.\mathrm{912}.\:\boldsymbol{{Evaluate}}\:\boldsymbol{{f}}\left(\mathrm{2}.\mathrm{279}\right)\:\boldsymbol{{by}}\:\boldsymbol{{first}}\:\boldsymbol{{calculating}} \\ $$$$\left(\mathrm{2}.\mathrm{279}\right)^{\mathrm{2}} ,\left(\mathrm{2}.\mathrm{279}\right)^{\mathrm{3}} ,\left(\mathrm{2}.\mathrm{279}\right)^{\mathrm{4}} \boldsymbol{{and}}\left(\mathrm{2}.\mathrm{279}\right)^{\mathrm{5}} \:\boldsymbol{{using}} \\ $$$$\boldsymbol{{four}}βˆ’\boldsymbol{{digit}}\:\boldsymbol{{round}}\:\boldsymbol{{arithmetic}}.\:\boldsymbol{{hence}},\boldsymbol{{compute}} \\ $$$$\boldsymbol{{the}}\:\boldsymbol{{absolute}}\:\boldsymbol{{and}}\:\boldsymbol{{relative}}\:\boldsymbol{{errors}}. \\ $$

Question Number 222829    Answers: 1   Comments: 0

If f(x) = ((3x + [x])/(2x)) Find lim_(xβ†’βˆ’5^+ ) f(x) βˆ’ lim_(xβ†’βˆ’5^βˆ’ ) f(x) = ?

$$\mathrm{If}\:\:\:\mathrm{f}\left(\mathrm{x}\right)\:=\:\frac{\mathrm{3x}\:+\:\left[\mathrm{x}\right]}{\mathrm{2x}} \\ $$$$\mathrm{Find}\:\:\:\underset{\boldsymbol{\mathrm{x}}\rightarrowβˆ’\mathrm{5}^{+} } {\mathrm{lim}}\:\mathrm{f}\left(\mathrm{x}\right)\:βˆ’\:\underset{\boldsymbol{\mathrm{x}}\rightarrowβˆ’\mathrm{5}^{βˆ’} } {\mathrm{lim}}\:\mathrm{f}\left(\mathrm{x}\right)\:=\:? \\ $$

Question Number 222801    Answers: 2   Comments: 0

Question Number 222777    Answers: 1   Comments: 0

Simplify: (((cos214Β° + i sin146Β°)βˆ™(cos10Β° + i sin10Β°))/((cos66Β° βˆ’ i sin246Β°))) = ?

$$\mathrm{Simplify}: \\ $$$$\frac{\left(\mathrm{cos214}Β°\:+\:\boldsymbol{\mathrm{i}}\:\mathrm{sin146}Β°\right)\centerdot\left(\mathrm{cos10}Β°\:+\:\boldsymbol{\mathrm{i}}\:\mathrm{sin10}Β°\right)}{\left(\mathrm{cos66}Β°\:βˆ’\:\boldsymbol{\mathrm{i}}\:\mathrm{sin246}Β°\right)}\:=\:? \\ $$

Question Number 222754    Answers: 1   Comments: 1

Question Number 222743    Answers: 1   Comments: 0

Compare: a = arcctg (√2) b = arccos ((√2)/2) c = arctg (√2)

$$\mathrm{Compare}: \\ $$$$\boldsymbol{\mathrm{a}}\:=\:\mathrm{arcctg}\:\sqrt{\mathrm{2}} \\ $$$$\boldsymbol{\mathrm{b}}\:=\:\mathrm{arccos}\:\frac{\sqrt{\mathrm{2}}}{\mathrm{2}} \\ $$$$\boldsymbol{\mathrm{c}}\:=\:\mathrm{arctg}\:\sqrt{\mathrm{2}} \\ $$

Question Number 222616    Answers: 1   Comments: 0

Question Number 222585    Answers: 3   Comments: 2

Question Number 222584    Answers: 0   Comments: 0

find the correct const. to preconst. β€œ x^n βˆ’2=βˆ’x ”

$${find}\:{the}\:{correct}\:{const}.\:{to}\:{preconst}.\:``\:{x}^{{n}} βˆ’\mathrm{2}=βˆ’{x}\:'' \\ $$

Question Number 222582    Answers: 2   Comments: 0

If: a_i > 0 , b_i > 0 , i = 1,...,n^(βˆ’) Prove that: (√(a_1 ^2 + b_1 ^2 )) + (√(a_2 ^2 + b_2 ^2 )) +...+ (√(a_n ^2 + b_n ^2 )) β‰₯ β‰₯ (√((a_1 +a_2 +...+a_n )^2 + (b_1 +b_2 +...+b_n )^2 ))

$$\mathrm{If}:\:\:\:\mathrm{a}_{\boldsymbol{\mathrm{i}}} \:>\:\mathrm{0}\:\:\:,\:\:\:\mathrm{b}_{\boldsymbol{\mathrm{i}}} \:>\:\mathrm{0}\:\:\:,\:\:\:\mathrm{i}\:=\:\overline {\mathrm{1},...,\mathrm{n}} \\ $$$$\mathrm{Prove}\:\mathrm{that}: \\ $$$$\sqrt{\mathrm{a}_{\mathrm{1}} ^{\mathrm{2}} \:+\:\mathrm{b}_{\mathrm{1}} ^{\mathrm{2}} }\:+\:\sqrt{\mathrm{a}_{\mathrm{2}} ^{\mathrm{2}} \:+\:\mathrm{b}_{\mathrm{2}} ^{\mathrm{2}} }\:+...+\:\sqrt{\mathrm{a}_{\boldsymbol{\mathrm{n}}} ^{\mathrm{2}} \:+\:\mathrm{b}_{\boldsymbol{\mathrm{n}}} ^{\mathrm{2}} }\:\:\:\geqslant \\ $$$$\geqslant\:\sqrt{\left(\mathrm{a}_{\mathrm{1}} +\mathrm{a}_{\mathrm{2}} +...+\mathrm{a}_{\boldsymbol{\mathrm{n}}} \right)^{\mathrm{2}} \:+\:\left(\mathrm{b}_{\mathrm{1}} +\mathrm{b}_{\mathrm{2}} +...+\mathrm{b}_{\boldsymbol{\mathrm{n}}} \right)^{\mathrm{2}} } \\ $$

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