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AlgebraQuestion and Answers: Page 222

Question Number 122857 Answers: 0 Comments: 0

Question Number 122854 Answers: 1 Comments: 0

Question Number 122821 Answers: 1 Comments: 0

Given { ((x^(ln x+ln y) = 5)),((y^(ln x+ln y) = 2)) :} then { ((x=?)),((y=?)) :}

$G i v e n {\begin{cases} x^{\ln x + \ln y} = 5 \\ y^{\ln x + \ln y} = 2 \end{cases}$ $t h e n {\begin{cases} x = ? \\ y = ? \end{cases}$

Question Number 122658 Answers: 0 Comments: 0

we are in C^3 . (S): { ((x+y+z=2i−1 and xyz=2)),((xy+yz+xz=−2(1+i) )) :} P(z)=z^3 +(1−2i)z^2 −2(1+i)−2. show that (a,b,c) is solution of (S) if and only a;b;c are roots of P.

$w e a r e i n C^{3} .$ $(S) : {\begin{cases} x + y + z = 2 i - 1 a n d x y z = 2 \\ x y + y z + x z = - 2 (1 + i) \end{cases}$ $P (z) = z^{3} + (1 - 2 i) z^{2} - 2 (1 + i) - 2 .$ $s h o w t h a t (a, b, c) i s s o l u t i o n$ $o f (S) i f a n d o n l y a; b; c a r e$ $r o o t s o f P .$

Question Number 122653 Answers: 1 Comments: 0

we define in base x the number y and z by: y=123^(−) ^(x ) and z=201^(−) ^x 1) without knowing x, write the product x×y×z in function of x. 2) we suppose that x+y+z=92 find x;y;z.

$w e d e f i n e i n b a s e x t h e$ $n u m b e r y a n d z b y :$ $y = \overset{―}{123}^{x} a n d z = \overset{―}{201}^{x}$ $1) w i t h o u t k n o w i n g x, w r i t e$ $t h e p r o d u c t x \times y \times z i n f u n c t i o n$ $o f x .$ $2) w e s u p p o s e t h a t x + y + z = 92$ $f i n d x; y; z .$

Question Number 122651 Answers: 1 Comments: 0

show that if 5^(3n) +5^(2n) +5^n +1 is divisible by 13, then n (∈ N) is not a multiple of 4.

$s h o w t h a t i f$ $5^{3 n} + 5^{2 n} + 5^{n} + 1 i s d i v i s i b l e b y$ $13, t h e n n (\in N) i s n o t a$ $m u l t i p l e o f 4 .$

Question Number 122649 Answers: 1 Comments: 2

By divising an integer a by integer b we find the result: 0.285714285714... followed by a group of 6 digits: 285714 which is repeated indefinited. determinate the fraction (a/b)

$B y d i v i s i n g a n i n t e g e r a b y$ $i n t e g e r b w e f i n d t h e r e s u l t :$ $0.285714285714 . . . f o l l o w e d$ $b y a g r o u p o f 6 d i g i t s : 285714$ $w h i c h i s r e p e a t e d i n d e f i n i t e d .$ $d e t e r m i n a t e t h e f r a c t i o n \frac{a}{b}$

Question Number 122648 Answers: 2 Comments: 0

Determinate the values of n ∈ N such that n−1 can divise 2n+3

$D e t e r m i n a t e t h e v a l u e s o f n \in N$ $s u c h t h a t n - 1 c a n d i v i s e 2 n + 3$

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

$p \in Z . g i v e n :$ $u = 14 p + 3; v = 5 p + 1,$ $(E) : 87 x + 31 y = 2; w e h a v e$ $a l s o t h e l i n e (D) : 87 x - 31 y = 2$ $1) s h o w t h a t u a n d v a r e p r i m e s$ $b e t w e e n t h e m . (i m e a n t h e$ ${d o n}^{'} t h a v e a n y c o m m o n d i v i s o r$ $e x c e p t e d 1 a n d - 1 .)$ $2) d e d u c t t h a t 87 a n d 31 a r e$ $p r i m e s b e t w e e n t h e m .$ $3) S o l v e (E) .$ $4) D e t e r m i n a t e p o i n t s (x; y) \in (D)$ $w h i c h t h a t t h e i r c o r d o n n a t e s$ $x; y \in N a n d x ⩽ 100$

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

$D e t e r m i n a t e t h e c o u p l e s$ $(a; b) s u c h t h a t$ $G C D (a; b) + L C M (a; b) = a + b$ $G C D : g r e a t e s t c o m m o n d i v i s o r$ $L C M : l e a s t c o m m o n m u l t i p l e$

Question Number 122640 Answers: 0 Comments: 0

f(f(x))=x^2 −1 find f(x)

$f (f (x)) = x^{2} - 1$ $f i n d f (x)$

Question Number 122580 Answers: 0 Comments: 3

Solve x^x =2x

$S o l v e$ $x^{x} = 2 x$

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.

$Given that I_{n} = \underset{0}{\int^{1}} x {(1 - x)}^{n} d x$ $obtain a reduction formulae for I_{n} in terms$ $of I_{n - 2} Hence evaluate \underset{0}{\int^{1}} x {(1 - x)}^{5} d x .$

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

$F i n d t h e n u m b e r o f t r i p l e t s (x / a / b) w h e r e x$ $i s a r e a l n u m b e r a n d (a / b) b e l o n g s t o t h e s e t$ ${1 / 2 / 3 / 4 / 5 / 6 / 7 / 8 / 9} s u c h t h a t$ $x^{2} - a {x} + b = 0$ $w h e r e {x} d e n o t e s t h e f r a c t i o n a l p a r t o f r e a l n u m b e r x$