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AlgebraQuestion and Answers: Page 259

Question Number 92146 Answers: 1 Comments: 1

how do i find integers that satisfy x^2 −y^2 =2017

$${how}\:{do}\:{i}\:{find}\:{integers}\:{that}\:{satisfy} \\ $$$${x}^{\mathrm{2}} −{y}^{\mathrm{2}} =\mathrm{2017} \\ $$

Question Number 92137 Answers: 0 Comments: 2

∫((2x)/(1+x))

$$\int\frac{\mathrm{2}{x}}{\mathrm{1}+{x}} \\ $$

Question Number 92102 Answers: 2 Comments: 3

how can we factorize x^5 −1 ?

$${how}\:{can}\:{we}\:{factorize}\:\:\:{x}^{\mathrm{5}} −\mathrm{1}\:\:? \\ $$

Question Number 92084 Answers: 1 Comments: 0

Question Number 92013 Answers: 1 Comments: 10

Solve: 2^x + 3^y = 72 ..... (i) 2^y + 3^x = 108 ..... (ii)

$$\mathrm{Solve}: \\ $$$$\:\:\:\mathrm{2}^{\mathrm{x}} \:\:+\:\:\mathrm{3}^{\mathrm{y}} \:\:\:=\:\:\mathrm{72}\:\:\:\:\:.....\:\left(\mathrm{i}\right) \\ $$$$\:\:\:\mathrm{2}^{\mathrm{y}} \:\:+\:\:\mathrm{3}^{\mathrm{x}} \:\:\:=\:\:\mathrm{108}\:\:\:\:\:.....\:\left(\mathrm{ii}\right) \\ $$

Question Number 92008 Answers: 0 Comments: 1

Sum of infinite series: 1 + (3/4) + ((3.5)/(4.8)) + ((3.5.7)/(4.8.12)) + ... is ?

$$\mathrm{Sum}\:\mathrm{of}\:\mathrm{infinite}\:\mathrm{series}:\:\:\mathrm{1}\:\:+\:\:\frac{\mathrm{3}}{\mathrm{4}}\:\:+\:\:\frac{\mathrm{3}.\mathrm{5}}{\mathrm{4}.\mathrm{8}}\:\:+\:\:\frac{\mathrm{3}.\mathrm{5}.\mathrm{7}}{\mathrm{4}.\mathrm{8}.\mathrm{12}}\:\:+\:\:...\:\:\:\:\mathrm{is}\:? \\ $$

Question Number 92000 Answers: 1 Comments: 0

proof 0!!=1

$$\mathrm{proof}\:\mathrm{0}!!=\mathrm{1} \\ $$

Question Number 91936 Answers: 0 Comments: 6

how to evaluate ln(i), i=(√(−1)).

$${how}\:{to}\:{evaluate}\:{ln}\left({i}\right),\:{i}=\sqrt{−\mathrm{1}}. \\ $$

Question Number 91872 Answers: 0 Comments: 3

solve in R 8(√(x^4 +1))+5(√(x^3 +1))=7x^2 +12

$${solve}\:{in}\:\mathbb{R} \\ $$$$\mathrm{8}\sqrt{\mathrm{x}^{\mathrm{4}} +\mathrm{1}}+\mathrm{5}\sqrt{\mathrm{x}^{\mathrm{3}} +\mathrm{1}}=\mathrm{7x}^{\mathrm{2}} +\mathrm{12} \\ $$

Question Number 91870 Answers: 0 Comments: 5

(1^ /x^(2x) ) + x^(−4x) = 6, (x ≠ 0) x = ?_

$$\:\frac{\overset{\:} {\mathrm{1}}}{\mathrm{x}^{\mathrm{2x}} }\:+\:\mathrm{x}^{−\mathrm{4x}} \:=\:\mathrm{6},\:\:\left(\mathrm{x}\:\neq\:\mathrm{0}\right) \\ $$$$\: \\ $$$$\:\mathrm{x}\:=\:\underset{\:} {?} \\ $$

Question Number 91850 Answers: 0 Comments: 3

Question Number 91843 Answers: 2 Comments: 5

{ (((1/x)+y = 2)),((x+(1/y) = 3)) :} find x^2 +y^2

$$\begin{cases}{\frac{\mathrm{1}}{{x}}+{y}\:=\:\mathrm{2}}\\{{x}+\frac{\mathrm{1}}{{y}}\:=\:\mathrm{3}}\end{cases} \\ $$$${find}\:{x}^{\mathrm{2}} +{y}^{\mathrm{2}} \\ $$

Question Number 91786 Answers: 0 Comments: 7

repost question from mr jagoll { ((2+6y = (x/y)−(√(x−2y)))),(((√(x+(√(x−2y)))) = x+3y−2 )) :}

$${repost}\:{question}\:{from} \\ $$$${mr}\:{jagoll} \\ $$$$\begin{cases}{\mathrm{2}+\mathrm{6}{y}\:=\:\frac{{x}}{{y}}−\sqrt{{x}−\mathrm{2}{y}}}\\{\sqrt{{x}+\sqrt{{x}−\mathrm{2}{y}}}\:=\:{x}+\mathrm{3}{y}−\mathrm{2}\:}\end{cases} \\ $$

Question Number 91732 Answers: 0 Comments: 2

Find the least possible value of x 8x ≡ 24 (mod 16) .... (i) 3x ≡ 6 (mod 25) .... (ii)

$$\mathrm{Find}\:\mathrm{the}\:\mathrm{least}\:\mathrm{possible}\:\mathrm{value}\:\mathrm{of}\:\:\mathrm{x} \\ $$$$\:\:\:\:\mathrm{8x}\:\equiv\:\mathrm{24}\:\left(\mathrm{mod}\:\mathrm{16}\right)\:\:\:\:\:....\:\left(\mathrm{i}\right) \\ $$$$\:\:\:\:\mathrm{3x}\:\equiv\:\mathrm{6}\:\left(\mathrm{mod}\:\mathrm{25}\right)\:\:\:\:\:\:....\:\left(\mathrm{ii}\right) \\ $$

Question Number 91744 Answers: 1 Comments: 1

Question Number 91688 Answers: 0 Comments: 2

solve equations x^(x ) + y^y = 31 and x + y = 5

$${solve}\:{equations}\:{x}^{{x}\:} +\:{y}^{{y}} \:=\:\mathrm{31}\:{and}\:{x}\:+\:{y}\:=\:\mathrm{5} \\ $$

Question Number 91660 Answers: 0 Comments: 4

Question Number 91647 Answers: 1 Comments: 0

solve x⌊x⌊x⌊x⌋⌋⌋=2020

$${solve} \\ $$$${x}\lfloor{x}\lfloor{x}\lfloor{x}\rfloor\rfloor\rfloor=\mathrm{2020} \\ $$

Question Number 91599 Answers: 0 Comments: 1

Question Number 91560 Answers: 0 Comments: 2

x=((1+(√(2004)))/2) 4x^3 −2007x−2000=?

$${x}=\frac{\mathrm{1}+\sqrt{\mathrm{2004}}}{\mathrm{2}} \\ $$$$\mathrm{4}{x}^{\mathrm{3}} −\mathrm{2007}{x}−\mathrm{2000}=? \\ $$

Question Number 91491 Answers: 1 Comments: 0

x^3 +1 = 2 ((2x−1))^(1/(3 )) x =?

$${x}^{\mathrm{3}} +\mathrm{1}\:=\:\mathrm{2}\:\sqrt[{\mathrm{3}\:\:}]{\mathrm{2}{x}−\mathrm{1}} \\ $$$${x}\:=? \\ $$

Question Number 91474 Answers: 0 Comments: 0

f(x)=(√(4−x^2 )) and g(x)=3x+1 find the sum , different, and product f(x) and g(x).

$$\mathrm{f}\left(\mathrm{x}\right)=\sqrt{\mathrm{4}−\mathrm{x}^{\mathrm{2}} }\:\:\mathrm{and}\:\mathrm{g}\left(\mathrm{x}\right)=\mathrm{3x}+\mathrm{1} \\ $$$$\mathrm{find}\:\mathrm{the}\:\mathrm{sum}\:,\:\mathrm{different},\:\mathrm{and}\:\mathrm{product} \\ $$$$\mathrm{f}\left(\mathrm{x}\right)\:\mathrm{and}\:\mathrm{g}\left(\mathrm{x}\right). \\ $$

Question Number 91473 Answers: 1 Comments: 0

Question Number 91471 Answers: 1 Comments: 0

∣2x−7∣>3

$$\mid\mathrm{2x}−\mathrm{7}\mid>\mathrm{3} \\ $$

Question Number 91470 Answers: 0 Comments: 2

∣x−3∣<0.1

$$\mid\mathrm{x}−\mathrm{3}\mid<\mathrm{0}.\mathrm{1} \\ $$

Question Number 91469 Answers: 0 Comments: 3

−5<((4−3x)/2)<l

$$−\mathrm{5}<\frac{\mathrm{4}−\mathrm{3x}}{\mathrm{2}}<\mathrm{l} \\ $$

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