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AlgebraQuestion and Answers: Page 234

Question Number 122647 Answers: 0 Comments: 0

p ∈ Z. given: u=14p+3 ; v=5p+1, (E):87x+31y=2 ; we have also the line (D): 87x−31y=2 1)show that u and v are primes between them.(i mean the don′t have any common divisor excepted 1 and −1.) 2)deduct that 87 and 31 are primes between them. 3)Solve (E). 4)Determinate points (x;y)∈ (D) which that their cordonnates x;y ∈ N and x≤100

$${p}\:\in\:\mathbb{Z}.\:{given}: \\ $$$${u}=\mathrm{14}{p}+\mathrm{3}\:;\:{v}=\mathrm{5}{p}+\mathrm{1}, \\ $$$$\left({E}\right):\mathrm{87}{x}+\mathrm{31}{y}=\mathrm{2}\:;\:{we}\:{have}\: \\ $$$${also}\:{the}\:{line}\:\left({D}\right):\:\mathrm{87}{x}−\mathrm{31}{y}=\mathrm{2} \\ $$$$\left.\mathrm{1}\right){show}\:{that}\:{u}\:{and}\:{v}\:{are}\:{primes} \\ $$$${between}\:{them}.\left({i}\:{mean}\:{the}\:\right. \\ $$$${don}'{t}\:{have}\:{any}\:{common}\:{divisor}\: \\ $$$$\left.{excepted}\:\mathrm{1}\:{and}\:−\mathrm{1}.\right) \\ $$$$\left.\mathrm{2}\right){deduct}\:{that}\:\mathrm{87}\:{and}\:\mathrm{31}\:{are} \\ $$$${primes}\:{between}\:{them}. \\ $$$$\left.\mathrm{3}\right){Solve}\:\left({E}\right). \\ $$$$\left.\mathrm{4}\right){Determinate}\:{points}\:\left({x};{y}\right)\in\:\left({D}\right)\: \\ $$$${which}\:{that}\:{their}\:{cordonnates} \\ $$$${x};{y}\:\in\:\mathbb{N}\:{and}\:{x}\leqslant\mathrm{100} \\ $$$$ \\ $$

Question Number 122646 Answers: 0 Comments: 4

Determinate the couples (a; b) such that GCD(a;b)+LCM(a;b)=a+b GCD: greatest common divisor LCM: least common multiple

$${Determinate}\:{the}\:{couples}\: \\ $$$$\left({a};\:{b}\right)\:{such}\:{that}\: \\ $$$${GCD}\left({a};{b}\right)+{LCM}\left({a};{b}\right)={a}+{b} \\ $$$${GCD}:\:{greatest}\:{common}\:{divisor} \\ $$$${LCM}:\:{least}\:{common}\:{multiple} \\ $$

Question Number 122640 Answers: 0 Comments: 0

f(f(x))=x^2 −1 find f(x)

$${f}\left({f}\left({x}\right)\right)={x}^{\mathrm{2}} −\mathrm{1} \\ $$$${find}\:{f}\left({x}\right) \\ $$

Question Number 122580 Answers: 0 Comments: 3

Solve x^x =2x

$${Solve} \\ $$$${x}^{{x}} =\mathrm{2}{x} \\ $$

Question Number 122551 Answers: 1 Comments: 0

Question Number 122523 Answers: 2 Comments: 0

Question Number 122445 Answers: 2 Comments: 0

Question Number 122360 Answers: 3 Comments: 0

Question Number 122214 Answers: 1 Comments: 0

Question Number 122166 Answers: 3 Comments: 0

Given that I_n = ∫_0 ^1 x(1−x)^n dx obtain a reduction formulae for I_(n ) in terms of I_(n−2) Hence evaluate ∫_0 ^1 x(1−x)^5 dx.

$$\mathrm{Given}\:\mathrm{that}\:{I}_{{n}} \:=\:\underset{\mathrm{0}} {\overset{\mathrm{1}} {\int}}{x}\left(\mathrm{1}−{x}\right)^{{n}} {dx} \\ $$$$\mathrm{obtain}\:\mathrm{a}\:\mathrm{reduction}\:\mathrm{formulae}\:\mathrm{for}\:{I}_{{n}\:} \:\mathrm{in}\:\mathrm{terms} \\ $$$$\mathrm{of}\:{I}_{{n}−\mathrm{2}} \:\mathrm{Hence}\:\mathrm{evaluate}\:\:\underset{\mathrm{0}} {\overset{\mathrm{1}} {\int}}{x}\left(\mathrm{1}−{x}\right)^{\mathrm{5}} {dx}. \\ $$

Question Number 122095 Answers: 0 Comments: 0

Find the number of triplets(x/a/b) where x is a real number and (a/b) belongs to the set {1/2/3/4/5/6/7/8/9} such that x^2 −a{x}+b =0 where {x} denotes the fractional part of real number x

$${Find}\:{the}\:\:{number}\:{of}\:{triplets}\left({x}/{a}/{b}\right)\:{where}\:{x} \\ $$$${is}\:{a}\:{real}\:{number}\:{and}\:\left({a}/{b}\right)\:{belongs}\:{to}\:{the}\:{set} \\ $$$$\left\{\mathrm{1}/\mathrm{2}/\mathrm{3}/\mathrm{4}/\mathrm{5}/\mathrm{6}/\mathrm{7}/\mathrm{8}/\mathrm{9}\right\}\:{such}\:{that}\: \\ $$$$ \\ $$$${x}^{\mathrm{2}} −{a}\left\{{x}\right\}+{b}\:=\mathrm{0} \\ $$$${where}\:\left\{{x}\right\}\:{denotes}\:{the}\:{fractional}\:{part}\:{of}\:{real}\:{number}\:{x} \\ $$$$ \\ $$$$ \\ $$

Question Number 122081 Answers: 2 Comments: 0

solve { ((∣x−1∣+∣y−1∣=1)),((∣x−1∣−y=−5)) :}

$$\:{solve}\:\begin{cases}{\mid{x}−\mathrm{1}\mid+\mid{y}−\mathrm{1}\mid=\mathrm{1}}\\{\mid{x}−\mathrm{1}\mid−{y}=−\mathrm{5}}\end{cases} \\ $$

Question Number 122075 Answers: 1 Comments: 0