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AlgebraQuestion and Answers: Page 277

Question Number 86141 Answers: 0 Comments: 5

A number n leaves a remainder of 22 when divided by 24 and remainder 30 when divided by 33. Find the least possible value of n

$$\mathrm{A}\:\mathrm{number}\:\mathrm{n}\:\mathrm{leaves}\:\mathrm{a}\:\mathrm{remainder}\:\mathrm{of}\:\:\mathrm{22}\:\:\mathrm{when}\:\mathrm{divided}\:\mathrm{by}\:\mathrm{24}\:\mathrm{and} \\ $$$$\mathrm{remainder}\:\:\mathrm{30}\:\:\mathrm{when}\:\mathrm{divided}\:\mathrm{by}\:\:\mathrm{33}.\:\:\mathrm{Find}\:\mathrm{the}\:\mathrm{least}\:\mathrm{possible} \\ $$$$\mathrm{value}\:\mathrm{of}\:\:\mathrm{n} \\ $$

Question Number 86085 Answers: 1 Comments: 4

If X^2 +Y^2 =10 XY=5 Find (X^2 −Y^2 )

$$\mathrm{If}\:\mathrm{X}^{\mathrm{2}} +\mathrm{Y}^{\mathrm{2}} =\mathrm{10} \\ $$$$\:\:\:\:\:\:\:\:\:\:\mathrm{XY}=\mathrm{5} \\ $$$$\mathrm{Find}\:\left(\mathrm{X}^{\mathrm{2}} −\mathrm{Y}^{\mathrm{2}} \right) \\ $$

Question Number 86042 Answers: 3 Comments: 0

solve: ⌊ (√x) ⌋=⌊(x/2)⌋

$${solve}:\:\:\lfloor\:\sqrt{{x}}\:\rfloor=\lfloor\frac{{x}}{\mathrm{2}}\rfloor \\ $$

Question Number 86009 Answers: 1 Comments: 0

solve in R :[(x/2)]+[((2x)/3)]−x=0

$${solve}\:{in}\:{R}\::\left[\frac{{x}}{\mathrm{2}}\right]+\left[\frac{\mathrm{2}{x}}{\mathrm{3}}\right]−{x}=\mathrm{0} \\ $$

Question Number 86000 Answers: 1 Comments: 0

solve the equation x^(1/3) =4

$${solve}\:{the}\:{equation}\:\mathrm{x}^{\frac{\mathrm{1}}{\mathrm{3}}} =\mathrm{4} \\ $$

Question Number 85930 Answers: 0 Comments: 1

Question Number 85902 Answers: 1 Comments: 15

find the coefficients of x^2 and x^3 terms in the expansion of (1+x)(1+2x)^2 (1+3x)^3 ...(1+100x)^(100)

$${find}\:{the}\:{coefficients}\:{of}\:{x}^{\mathrm{2}} \:{and}\:{x}^{\mathrm{3}} \: \\ $$$${terms}\:{in}\:{the}\:{expansion}\:{of} \\ $$$$\left(\mathrm{1}+{x}\right)\left(\mathrm{1}+\mathrm{2}{x}\right)^{\mathrm{2}} \left(\mathrm{1}+\mathrm{3}{x}\right)^{\mathrm{3}} ...\left(\mathrm{1}+\mathrm{100}{x}\right)^{\mathrm{100}} \\ $$

Question Number 85871 Answers: 0 Comments: 3

Question Number 85864 Answers: 1 Comments: 0

simplify the expression (√(6+2(√(8(√3)−10)))) − (√(7−(√3))) in the form (√((√a)+b)) ?

$${simplify}\:{the}\:{expression} \\ $$$$\sqrt{\mathrm{6}+\mathrm{2}\sqrt{\mathrm{8}\sqrt{\mathrm{3}}−\mathrm{10}}}\:−\:\sqrt{\mathrm{7}−\sqrt{\mathrm{3}}}\:\:{in} \\ $$$${the}\:{form}\:\sqrt{\sqrt{{a}}+{b}}\:? \\ $$

Question Number 85854 Answers: 0 Comments: 2

If x,y,z ∈ R satisfy the equation x^4 + y^4 + z^4 = 4xyz −1 find minimum value of x + y + z

$$\mathrm{If}\:\mathrm{x},\mathrm{y},\mathrm{z}\:\in\:\mathbb{R}\:\mathrm{satisfy}\:\mathrm{the}\:\mathrm{equation} \\ $$$$\mathrm{x}^{\mathrm{4}} \:+\:\mathrm{y}^{\mathrm{4}} \:+\:\mathrm{z}^{\mathrm{4}} \:=\:\mathrm{4xyz}\:−\mathrm{1}\: \\ $$$$\mathrm{find}\:\mathrm{minimum}\:\mathrm{value}\:\mathrm{of} \\ $$$$\mathrm{x}\:+\:\mathrm{y}\:+\:\mathrm{z}\: \\ $$

Question Number 85822 Answers: 2 Comments: 1

how to solve ((x−1))^(1/(3 )) + ((x−3))^(1/(3 )) + ((x−5))^(1/(3 )) = 0

$$\mathrm{how}\:\mathrm{to}\:\mathrm{solve}\: \\ $$$$\sqrt[{\mathrm{3}\:\:}]{\mathrm{x}−\mathrm{1}}\:+\:\sqrt[{\mathrm{3}\:\:}]{\mathrm{x}−\mathrm{3}}\:+\:\sqrt[{\mathrm{3}\:\:}]{\mathrm{x}−\mathrm{5}}\:=\:\mathrm{0}\: \\ $$

Question Number 85779 Answers: 0 Comments: 0

Question Number 85762 Answers: 0 Comments: 12

Question Number 85756 Answers: 0 Comments: 5

Question Number 85729 Answers: 0 Comments: 6

if march 24, 2020 is Tuesday, then march 24, 2032 is the day ?

$$\mathrm{if}\:\mathrm{march}\:\mathrm{24},\:\mathrm{2020}\:\mathrm{is}\:\mathrm{Tuesday}, \\ $$$$\mathrm{then}\:\mathrm{march}\:\mathrm{24},\:\mathrm{2032}\:\mathrm{is}\:\mathrm{the}\:\mathrm{day}\:? \\ $$

Question Number 85696 Answers: 0 Comments: 0

Montrer que: (√5)+(√(30))+(√(50))<(√(10))+(√(20))+(√(60)) {niveau second)

$$\mathrm{Montrer}\:\mathrm{que}: \\ $$$$\sqrt{\mathrm{5}}+\sqrt{\mathrm{30}}+\sqrt{\mathrm{50}}<\sqrt{\mathrm{10}}+\sqrt{\mathrm{20}}+\sqrt{\mathrm{60}} \\ $$$$\left\{\mathrm{niveau}\:\mathrm{second}\right) \\ $$

Question Number 85664 Answers: 0 Comments: 2

Show that a group order 100 is not simple

$$\boldsymbol{{S}\mathrm{how}}\:\boldsymbol{\mathrm{that}}\:\boldsymbol{\mathrm{a}}\:\boldsymbol{\mathrm{group}}\:\boldsymbol{\mathrm{order}}\:\mathrm{100}\:\boldsymbol{\mathrm{is}}\:\boldsymbol{\mathrm{not}}\:\boldsymbol{\mathrm{simple}} \\ $$

Question Number 85655 Answers: 0 Comments: 0

Question Number 85624 Answers: 0 Comments: 0

Question Number 85554 Answers: 0 Comments: 1

2x^2 +5x+7=0

$$\mathrm{2}{x}^{\mathrm{2}} +\mathrm{5}{x}+\mathrm{7}=\mathrm{0} \\ $$

Question Number 85532 Answers: 1 Comments: 0

Find the term independent of x in the expression of (2x−(1/(2x)))^9

$${Find}\:{the}\:{term}\:{independent}\:{of}\:\boldsymbol{\mathrm{x}}\:{in}\:{the}\:{expression}\:{of}\:\left(\mathrm{2}{x}−\frac{\mathrm{1}}{\mathrm{2}{x}}\right)^{\mathrm{9}} \\ $$

Question Number 85490 Answers: 0 Comments: 3

Given that the expression 2x^3 +px^2 −8x+9 is exactly divisable by x^2 −6x+5, find the value of p and q. Hence factorise the expression fully

$${Given}\:{that}\:{the}\:{expression}\:\mathrm{2}{x}^{\mathrm{3}} +{px}^{\mathrm{2}} −\mathrm{8}{x}+\mathrm{9}\:{is}\:{exactly}\:{divisable}\:{by}\:{x}^{\mathrm{2}} −\mathrm{6}{x}+\mathrm{5},\:{find}\:{the}\:{value}\:{of}\:\boldsymbol{\mathrm{p}}\:{and}\:\boldsymbol{\mathrm{q}}.\:{Hence}\:{factorise}\:{the}\:{expression}\:{fully} \\ $$

Question Number 85418 Answers: 0 Comments: 1

Find the term indepent of x in the expression of (2x−(1/(2x)))^9

$${Find}\:{the}\:{term}\:{indepent}\:{of}\:{x}\:{in}\:{the}\:{expression}\:{of}\:\left(\mathrm{2}{x}−\frac{\mathrm{1}}{\mathrm{2}{x}}\right)^{\mathrm{9}} \\ $$

Question Number 85413 Answers: 0 Comments: 0

Question Number 85412 Answers: 0 Comments: 1

Question Number 85365 Answers: 3 Comments: 0

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