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AlgebraQuestion and Answers: Page 97

Question Number 176514 Answers: 1 Comments: 0

△ABC, sinA=cosB=tanC find the value of cos^3 A+cos^2 A−cosA.

$△ A B C, \sin A = \cos B = \tan C$ $find the value of \cos^{3} A + \cos^{2} A - \cos A .$

Question Number 176513 Answers: 1 Comments: 0

z∈C, ((z−3i)/(z+i))∈R^− , ((z−3)/(z+1))∈I find z.

$z \in C, \frac{z - 3 i}{z + i} \in R^{-}, \frac{z - 3}{z + 1} \in I$ $find z .$

Question Number 176485 Answers: 2 Comments: 1

Question Number 176482 Answers: 0 Comments: 0

L(E) est l′algebre des endomorphisme continus d′un espace de Banach E, muni de la norme d′application lineaire ; GL(E) est le sous ensemble des elements inversibles de L(E) a)Montrer que GL(E) est ouvert dans L(E) b)montrer que l′application ∅:GL(E)→GL(E) u→u^(−1) =∅(u) est continu dans GL(E) c)montrer que ∅ est differentiable dans GL(E) dt calculer d∅

$L (E) e s t l^{'} a l g e b r e d e s e n d o m o r p h i s m e$ $c o n t i n u s d^{'} u n e s p a c e d e B a n a c h E,$ $m u n i d e l a n o r m e d^{'} a p p l i c a t i o n l i n e a i r e$ $; G L (E) e s t l e s o u s e n s e m b l e d e s$ $e l e m e n t s i n v e r s i b l e s d e L (E)$ $a) M o n t r e r q u e G L (E) e s t o u v e r t d a n s$ $L (E)$ $b) m o n t r e r q u e l^{'} a p p l i c a t i o n$ $\emptyset : G L (E) \to G L (E)$ $u \to u^{- 1} = \emptyset (u) e s t c o n t i n u d a n s G L (E)$ $c) m o n t r e r q u e \emptyset e s t d i f f e r e n t i a b l e$ $d a n s G L (E) d t c a l c u l e r d \emptyset$

Question Number 176472 Answers: 1 Comments: 0

solve for x,y,z with x+y+z=x^2 +y^2 +z^2 =x^3 +y^3 +z^3 =5

$s o l v e f o r x, y, z w i t h$ $x + y + z = x^{2} + y^{2} + z^{2} = x^{3} + y^{3} + z^{3} = 5$

Question Number 176458 Answers: 5 Comments: 0

x^2 +x=1 ((x^5 +8)/(x+1))=?

$x^{2} + x = 1$ $\frac{x^{5} + 8}{x + 1} = ?$

Question Number 176453 Answers: 2 Comments: 0

If , α , β , γ ∈ ( 0 , 1 ) , then prove that : (√((1−^ α ).(1−^ β ). (1−^ γ ))) +(√(α^ .β^ .γ^ )) < 1

$I f, α, β, γ \in (0, 1), t h e n$ $p r o v e t h a t :$ $\sqrt{(1 \overset{}{-} α) . (1 \overset{}{-} β) . (1 \overset{}{-} γ)} + \sqrt{\overset{}{α} . \overset{}{β} . \overset{}{γ}} < 1$

Question Number 176448 Answers: 0 Comments: 3

Suppose a^3 +b^3 +c^3 =a^2 +b^2 +c^2 =a+b+c Prove that abc=0

$Suppose a^{3} + b^{3} + c^{3} = a^{2} + b^{2} + c^{2}$ $= a + b + c Prove that abc = 0$

Question Number 176427 Answers: 0 Comments: 0

Question Number 176423 Answers: 1 Comments: 0

Question Number 176387 Answers: 4 Comments: 5

x^3 +(1/x^3 ) = 1 ⇒(([x^5 +(1/x^5 )]^3 −1)/(x^5 +(1/x^5 ))) =?

$x^{3} + \frac{1}{x^{3}} = 1 \Rightarrow \frac{{[x^{5} + \frac{1}{x^{5}}]}^{3} - 1}{x^{5} + \frac{1}{x^{5}}} = ?$

Question Number 176384 Answers: 2 Comments: 0

Find the constant term in the expansion of the expression (2+3x)^3 ((1/x)−4)^4

$F i n d t h e c o n s t a n t t e r m i n t h e$ $e x p a n s i o n o f t h e e x p r e s s i o n$ ${(2 + 3 x)}^{3} {(\frac{1}{x} - 4)}^{4}$

Question Number 176393 Answers: 1 Comments: 0

show that 1+2+3+4+................ ∞ = ((−1)/8)

$s h o w t h a t$ $1 + 2 + 3 + 4 + . . . . . . . . . . . . . . . . \infty = \frac{- 1}{8}$

Question Number 176391 Answers: 2 Comments: 1

Question Number 176365 Answers: 1 Comments: 0

In △ABC the following relationship holds: Σ_(cyc) (a^2 /(b^2 + c^2 )) + 4 Π_(cyc) cos A ≤ 2

$In △ ABC the following relationship holds :$ $\sum_{cyc} \frac{a^{2}}{b^{2} + c^{2}} + 4 \prod_{cyc} \cos A ⩽ 2$

Question Number 176327 Answers: 0 Comments: 0

p(x)=2x^2 +(√(4x^2 )) pq=4 and p+q=2 faind p^a_2 +q^a_1 =?

$p (x) = 2 x^{2} + \sqrt{4 x^{2}}$ $p q = 4 a n d p + q = 2 f a i n d$ $p^{a_{2}} + q^{a_{1}} = ?$

Question Number 176347 Answers: 1 Comments: 0

(2+(1/4)x^2 )^5 (2−(1/3)x^2 )^5 find coefficient x^2

${(2 + \frac{1}{4} x^{2})}^{5} {(2 - \frac{1}{3} x^{2})}^{5}$ $find coefficient x^{2}$

Question Number 176303 Answers: 1 Comments: 0

Question Number 176300 Answers: 1 Comments: 4

coeffisien x^(2 ) from (2+(1/4)x^2 )^5 (1−4x)^5

$coeffisien x^{2} from {(2 + \frac{1}{4} x^{2})}^{5} {(1 - 4 x)}^{5}$

Question Number 176773 Answers: 0 Comments: 2

Let a, b, c >0. If ((a−b)/b)>7, ((b+c)/c)<8, Find min(a+b+c)

$Let a, b, c > 0 . If$ $\frac{a - b}{b} > 7, \frac{b + c}{c} < 8,$ $Find \min (a + b + c)$

Question Number 176279 Answers: 1 Comments: 0

Proof that : ∄n∈Z, n^2 +1≡0(mod 4)

$Proof that :$ $∄ n \in Z, n^{2} + 1 \equiv 0 (\mod 4)$

Question Number 176276 Answers: 2 Comments: 0

coeff of x^2 from [6+8x−(3/2)x^2 ]^5

$coeff of x^{2} from$ ${[6 + 8 x - \frac{3}{2} x^{2}]}^{5}$

Question Number 176206 Answers: 1 Comments: 0

Question Number 176189 Answers: 1 Comments: 0

solve for x (1+(1/x))^(x+1) =(1+(1/6))^6 show working

$s o l v e f o r x$ ${(1 + \frac{1}{x})}^{x + 1} = {(1 + \frac{1}{6})}^{6}$ $s h o w w o r k i n g$

Question Number 176159 Answers: 1 Comments: 0

Question Number 176155 Answers: 2 Comments: 3

Find how many distinct integers are there in this sequence: ⌊((1^2 +1)/(100))⌋, ⌊((2^2 +2)/(100))⌋, ⌊((3^2 +3)/(100))⌋, ..., ⌊((100^2 +100)/(100))⌋ where ⌊x⌋ is the greatest integer that is less than or equal to x

$Find how many distinct integers are there in this sequence :$ $⌊ \frac{1^{2} + 1}{100} ⌋, ⌊ \frac{2^{2} + 2}{100} ⌋, ⌊ \frac{3^{2} + 3}{100} ⌋, . . ., ⌊ \frac{100^{2} + 100}{100} ⌋$ $where ⌊ x ⌋ is the greatest integer that is less than or equal to x$

Pg 92 Pg 93 Pg 94 Pg 95 Pg 96 Pg 97 Pg 98 Pg 99 Pg 100 Pg 101

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