Question and Answers Forum

All Questions Topic List

AlgebraQuestion and Answers: Page 57

Question Number 194844 Answers: 1 Comments: 0

(x^2 +1)^2 +(x+3)^2 =(x^2 +ax+b)(x^2 +cx+d) Find a,b,c,d.

${(x^{2} + 1)}^{2} + {(x + 3)}^{2} = (x^{2} + a x + b) (x^{2} + c x + d)$ $F i n d a, b, c, d .$

Question Number 194837 Answers: 2 Comments: 0

for x>0 find the minimum of the function f(x)=x^3 +(5/x).

$f o r x > 0 f i n d t h e m i n i m u m o f t h e$ $f u n c t i o n f (x) = x^{3} + \frac{5}{x} .$

Question Number 194851 Answers: 0 Comments: 1

Name Zainab Bibi BC200400692 Assignmeng No#2 Mth 621 solution.. a_n =(((n− )!)/((n+ )^2 )) a_(n+ ) =(((n+ − )!)/((n+ + )^2 ))=(((n)!)/((n+2)^2 )) by ratio test (a_(n+ ) /a_n )=((((n)!)/((n+2)))/(((n− )!)/((n+ )^2 )))=(((n)!)/((n+2)^2 ))×(((n+ )^2 )/((n+ )!)) lim_(n→∞) (a_(n+ ) /a_n )=lim_(n→∞) ((n(n− )!)/((n+2)^2 ))×(((n+ )^2 )/((n− )!)) ∵(n)!=n(n− )! lim_(n→∞) (a_(n+ ) /a_n )=lim_(n→∞) ((n(n+ )^2 )/((n+2)^2 ))=lim_(n→∞) ((n(n^2 +1+2n))/(n^2 +4+4n)) lim_(n→∞) (((n^3 +n+2n^2 ))/(n^2 +4+4n))=lim_(n→∞) (((1+(1/n^2 )+(2/n)))/((1/n)+(1/n^3 )+(4/n^2 ))) Divided by n^3 to numerator and denominator Now by Applying limit (((1+(1/∞^(2 ) )+(2/∞)))/((1/∞)+(4/∞^3 )+(4/∞^2 )))=((1+0+0)/(0+0+0))=(1/0)=∞ lim_(n→∞) (a_(n+1) /a_n )=∞

Question Number 194809 Answers: 2 Comments: 0

If f(x)=ax^2 −5x+3 and g(x)=3x−3 intersection at points (1,h) and (3,t). Find

$I f f (x) = {a x}^{2} - 5 x + 3 a n d$ $g (x) = 3 x - 3 i n t e r s e c t i o n a t$ $p o i n t s (1, h) a n d (3, t) .$ $F i n d \underset{―}{}$

Question Number 194808 Answers: 0 Comments: 4

suppose a,b,c are positive real numbers prove the inequality (((a+b)/2))(((b+c)/2))(((c+a)/2))≥(((a+b+c)/3))(((abc)^2 ))^(1/3)

$s u p p o s e a, b, c a r e p o s i t i v e r e a l n u m b e r s$ $p r o v e t h e i n e q u a l i t y$ $(\frac{a + b}{2}) (\frac{b + c}{2}) (\frac{c + a}{2}) ⩾ (\frac{a + b + c}{3}) \sqrt[3]{{(a b c)}^{2}}$

Question Number 194791 Answers: 1 Comments: 0

$\underset{―}{\underset{⏟}{x}}$

Question Number 194779 Answers: 1 Comments: 4

If a divided by b gives q remaining r Then (a/b) = q,rrr... in base b+1

$I f a d i v i d e d b y b g i v e s q r e m a i n i n g r$ $T h e n \frac{a}{b} = q, r r r . . . i n b a s e b + 1$

Question Number 194756 Answers: 3 Comments: 0

$\underset{⏟}{b}$

Question Number 194710 Answers: 0 Comments: 21

let p be a prime number & let a_1 ,a_2 ,a_3 ,...,a_(p ) be integers show that , there exists an integer k such that the numbers a_1 +k, a_2 +k,a_3 +k,....,a_p +k produce at least (1/2)p distinct remainders when divided by p.

$l e t p b e a p r i m e n u m b e r$ $& l e t a_{1}, a_{2}, a_{3}, . . ., a_{p} b e i n t e g e r s$ $s h o w t h a t, t h e r e e x i s t s a n i n t e g e r k s u c h t h a t t h e n u m b e r s$ $a_{1} + k, a_{2} + k, a_{3} + k, . . . ., a_{p} + k$ $p r o d u c e a t l e a s t \frac{1}{2} p d i s t i n c t r e m a i n d e r s$ $w h e n d i v i d e d b y p .$

Question Number 194695 Answers: 1 Comments: 0

⇃

$⇃ \underset{―}{}$

Question Number 194648 Answers: 3 Comments: 3

Question Number 194637 Answers: 4 Comments: 1

x+y=1 x^2 +y^2 =2 x^(11) +y^(11) =?

$x + y = 1$ $x^{2} + y^{2} = 2$ $x^{11} + y^{11} = ?$

Question Number 194636 Answers: 0 Comments: 3

Question Number 194634 Answers: 1 Comments: 0

a_1 ,a_2 ,a_3 ,....,a_n >0 such that a_i ∈[0,i] ∀ i∈{1,2,3,4,...,n} prove that 2^n .a_1 (a_1 +a_2 )...(a_1 +a_2 +...+a_n )≥(n+1)(a_1 ^2 .a_2 ^2 ...a_n ^2 )

$a_{1}, a_{2}, a_{3}, . . . ., a_{n} > 0 s u c h t h a t a_{i} \in [0, i]$ $\forall i \in {1, 2, 3, 4, . . ., n} p r o v e t h a t$ $2^{n} . a_{1} (a_{1} + a_{2}) . . . (a_{1} + a_{2} + . . . + a_{n}) ⩾ (n + 1) (a_{1}^{2} . a_{2}^{2} . . . a_{n}^{2})$

Question Number 194619 Answers: 1 Comments: 0

Find the sum of the roots of the equation: −3x^3 + 8x^2 − 6x − 7 = 0

$Find the sum of the roots of the$ $equation :$ $- {3 x}^{3} + {8 x}^{2} - 6 x - 7 = 0$

Question Number 194612 Answers: 1 Comments: 2

Question Number 194610 Answers: 1 Comments: 0

where can I learn about multiple sigma notaions of dependent and independent variables something like this Σ_(1≤i) Σ_(<j) Σ_(<k≤1) (i+j+k)=λ find λ I want to know what to study

$w h e r e c a n I l e a r n a b o u t m u l t i p l e s i g m a n o t a i o n s$ $o f d e p e n d e n t a n d i n d e p e n d e n t v a r i a b l e s$ $s o m e t h i n g l i k e t h i s$ $\sum_{1 ⩽ i} \sum_{< j} \sum_{< k ⩽ 1} (i + j + k) = λ$ $f i n d λ$ $I w a n t t o k n o w w h a t t o s t u d y$