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AlgebraQuestion and Answers: Page 329

Question Number 32047 Answers: 0 Comments: 1

Question Number 32002 Answers: 1 Comments: 0

If z^3 =z^ prove then ∣z∣=1.

$I f z^{3} = \bar{z} p r o v e$ $t h e n ∣ z ∣= 1 .$

Question Number 31991 Answers: 0 Comments: 1

g_n =(√(g_(n−1) +g_(n−2) )) g_1 =1 g_2 =3 g_n =..

$g_{n} = \sqrt{g_{n - 1} + g_{n - 2}}$ $g_{1} = 1$ $g_{2} = 3$ $g_{n} = . .$

Question Number 31990 Answers: 1 Comments: 3

a_n =2a_(n−1) +3a_(n−2) a_0 =1 a_1 =2 a_n =...

$a_{n} = 2 a_{n - 1} + 3 a_{n - 2}$ $a_{0} = 1$ $a_{1} = 2$ $a_{n} = . . .$

Question Number 31963 Answers: 0 Comments: 0

find Re (((1+e^(iα) )/(1+e^(iβ) ))) and Im ( ((1+e^(iα) )/(1+e^(iβ) )) ) .

$f i n d R e (\frac{1 + e^{i α}}{1 + e^{i β}}) a n d I m (\frac{1 + e^{i α}}{1 + e^{i β}}) .$

Question Number 31927 Answers: 1 Comments: 0

The number of distinct real roots of equation x^4 −4x^3 +12x^2 +x−1=0.

$T h e n u m b e r o f d i s t i n c t r e a l r o o t s$ $o f e q u a t i o n x^{4} - 4 x^{3} + 12 x^{2} + x - 1 = 0 .$

Question Number 31915 Answers: 1 Comments: 3

If : (x^2 +x+2)^2 −(a−3)(x^2 +x+1)(x^2 +x+2) + (a−4)(x^2 +x+1)^2 =0 has at least one root , then find complete set of values of a.

$I f :$ ${(x^{2} + x + 2)}^{2} - (a - 3) (x^{2} + x + 1) (x^{2} + x + 2)$ $+ (a - 4) {(x^{2} + x + 1)}^{2} = 0 h a s a t l e a s t$ $o n e r o o t, t h e n f i n d c o m p l e t e s e t o f$ $v a l u e s o f a .$

Question Number 31895 Answers: 0 Comments: 3

Question Number 32372 Answers: 1 Comments: 0

Question Number 31868 Answers: 0 Comments: 0

Let a>b>1 be positive integers with b odd. Let n be a positive integer as well. If b^n divides a^n −1, prove that a^b > (3^n /n). Solution please. Thanks in advance!!

$L e t a > b > 1 b e p o s i t i v e i n t e g e r s w i t h b o d d .$ $L e t n b e a p o s i t i v e i n t e g e r a s w e l l . I f b^{n} d i v i d e s$ $a^{n} - 1, p r o v e t h a t a^{b} > \frac{3^{n}}{n} .$ $S o l u t i o n p l e a s e . T h a n k s i n a d v a n c e!!$

Question Number 31865 Answers: 1 Comments: 6

Range of function : f(x)= 6^x +3^x +6^(−x) +3^(−x) +2.

$R a n g e o f f u n c t i o n :$ $f (x) = 6^{x} + 3^{x} + 6^{- x} + 3^{- x} + 2 .$

Question Number 31864 Answers: 1 Comments: 0

Let S_n = Σ_(k=1) ^(4n) (−1)^((k(k+1))/2) k^2 . Then S_n can take the value(s) 1) 1056 2) 1088 3) 1120 4) 1332.

$L e t S_{n} = \underset{k = 1}{\sum^{4 n}} {(- 1)}^{\frac{k (k + 1)}{2}} k^{2} .$ $T h e n S_{n} c a n t a k e t h e v a l u e (s)$ $1) 1056$ $2) 1088$ $3) 1120$ $4) 1332 .$

Question Number 31804 Answers: 1 Comments: 0

A quadratic equation p(x)=0 having coefficient of x^2 unity is such that p(x)=0 and p(p(p(x)))=0 have a common root then, prove that : p(0)×p(1)=0.

$A q u a d r a t i c e q u a t i o n p (x) = 0 h a v i n g$ $c o e f f i c i e n t o f x^{2} u n i t y i s s u c h t h a t$ $p (x) = 0 a n d p (p (p (x))) = 0 h a v e a$ $c o m m o n r o o t t h e n,$ $p r o v e t h a t : p (0) \times p (1) = 0 .$

Question Number 31771 Answers: 1 Comments: 1

Consider a sequence in the form of groups (1),(2,2),(3,3,3),(4,4,4,4), (5,5,5,5,5),............ then the 2000th term of the above sequence is : ?

$C o n s i d e r a s e q u e n c e i n t h e f o r m o f$ $g r o u p s (1), (2, 2), (3, 3, 3), (4, 4, 4, 4),$ $(5, 5, 5, 5, 5), . . . . . . . . . . . .$ $t h e n t h e 2000 t h t e r m o f t h e a b o v e$ $s e q u e n c e i s : ?$

Question Number 31763 Answers: 3 Comments: 0

please find the integral solutions (x and y) (xy−7)^2 =x^2 +y^2

$p l e a s e f i n d t h e i n t e g r a l s o l u t i o n s (x a n d y)$ ${(x y - 7)}^{2} = x^{2} + y^{2}$

Question Number 31726 Answers: 1 Comments: 3

Let a_1 = (1/2) , a_(k+1) =a_k ^2 +a_k ∀ k≥ 1. then a_(101) is greater than a) 1 b) 2 c) 3 d) 4 .

$L e t a_{1} = \frac{1}{2}, a_{k + 1} = a_{k}^{2} + a_{k} \forall k ⩾ 1 .$ $t h e n a_{101} i s g r e a t e r t h a n$ $a) 1$ $b) 2$ $c) 3$ $d) 4 .$

Question Number 31677 Answers: 1 Comments: 0

24x^3 −26x^2 +9x−1=0(solve)

$24 x^{3} - 26 x^{2} + 9 x - 1 = 0 (s o l v e)$

Question Number 31670 Answers: 1 Comments: 0

how many roots from equation ae^x =1+x+(x^2 /2) from a>0 ?

$how many roots from equation$ ${a e}^{x} = 1 + x + \frac{x^{2}}{2}$ $f r o m a > 0 ?$

Question Number 31642 Answers: 0 Comments: 1

∼ Equivalence relation (a∼b & c≁b)⇒c≁a True or false and why

$\sim Equivalence relation$ $(a \sim b & c ≁ b) \Rightarrow c ≁ a$ $True or false and why$

Question Number 31596 Answers: 2 Comments: 2

Question Number 31595 Answers: 2 Comments: 2

Question Number 31594 Answers: 1 Comments: 0

Question Number 31591 Answers: 1 Comments: 4

Question Number 31542 Answers: 0 Comments: 0

let p(x)=(1+x+x^2 )^n −(1−x+x^2 )^n ∈C[x] 1) find the roots of p(x) 2) factorize p(x) inside C[x].

$l e t p (x) = {(1 + x + x^{2})}^{n} - {(1 - x + x^{2})}^{n} \in C [x]$ $1) f i n d t h e r o o t s o f p (x)$ $2) f a c t o r i z e p (x) i n s i d e C [x] .$

Question Number 31499 Answers: 0 Comments: 1

find the polynial p wich verify p(x)−p^′ (x)=x^n then calculate ∫_0 ^1 p(x)dx.

$f i n d t h e p o l y n i a l p w i c h v e r i f y p (x) - p^{^{'}} (x) = x^{n} t h e n$ $c a l c u l a t e \int_{0}^{1} p (x) d x .$

Question Number 31498 Answers: 0 Comments: 0

find tbe value of Π_(k=1) ^n sin(((kπ)/(n+1))).

$f i n d t b e v a l u e o f \prod_{k = 1}^{n} s i n (\frac{k π}{n + 1}) .$

Pg 324 Pg 325 Pg 326 Pg 327 Pg 328 Pg 329 Pg 330 Pg 331 Pg 332 Pg 333

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