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Question Number 37414 Answers: 1 Comments: 0

x^x =2 find the value of x.

$x^{x} = 2$ $f i n d t h e v a l u e o f x .$

Question Number 37411 Answers: 1 Comments: 0

((√(2)^(√2) ))

$(\sqrt{{2)}^{\sqrt{2}}}$

Question Number 37324 Answers: 0 Comments: 3

Question Number 37232 Answers: 0 Comments: 0

let A = (((1 −1 0)),((−1 1 1)) ) (0 0 3 ) calculate A^n .

$l e t A = (\begin{matrix} 1 - 1 0 \\ - 1 1 1 \end{matrix})$ $(0 0 3)$ $c a l c u l a t e A^{n} .$

Question Number 37231 Answers: 0 Comments: 0

let A = (((0 1 1)),((1 0 1)) ) (1 1 0 ) 1) calculate p_c (A) the caracteristic polunom of A 2) calculate A^n with n integr natural 3) calcypulate e^(tA) t∈ R

$l e t A = (\begin{matrix} 0 1 1 \\ 1 0 1 \end{matrix})$ $(1 1 0)$ $1) c a l c u l a t e p_{c} (A) t h e c a r a c t e r i s t i c$ $p o l u n o m o f A$ $2) c a l c u l a t e A^{n} w i t h n i n t e g r n a t u r a l$ $3) c a l c y p u l a t e e^{t A} t \in R$

Question Number 37230 Answers: 0 Comments: 0

let A = (((1 −2)),((1 4)) ) calculate A^n 2) find e^A , e^(−A) 3) find e^(iA) , e^(−iA) and e^(iA) +e^(−iA) .

$l e t A = (\begin{matrix} 1 - 2 \\ 1 4 \end{matrix})$ $c a l c u l a t e A^{n}$ $2) f i n d e^{A}, e^{- A}$ $3) f i n d e^{i A}, e^{- i A} a n d e^{i A} + e^{- i A} .$

Question Number 37228 Answers: 0 Comments: 0

E id k vectorial space and f∈L(E) 1)prove that if f is nilpotent with indice p≥1 ,I −f is bijective and (I−f)^(−1) =Σ_(i=0) ^(p−1) f^i 2)let E=R_n [x] and f∈L(E) / f(p) =p−p^′ prove that f is inversible and find f^(−1) .

$E i d k v e c t o r i a l s p a c e a n d f \in L (E)$ $1) p r o v e t h a t i f f i s n i l p o t e n t w i t h i n d i c e$ $p ⩾ 1, I - f i s b i j e c t i v e a n d$ ${(I - f)}^{- 1} = \sum_{i = 0}^{p - 1} f^{i}$ $2) l e t E = R_{n} [x] a n d f \in L (E) /$ $f (p) = p - p^{^{'}} p r o v e t h a t f i s i n v e r s i b l e$ $a n d f i n d f^{- 1} .$

Question Number 37166 Answers: 0 Comments: 2

if 3x^2 +2αxy+2y^2 +2ax−4y+1 can be resolved into two linear factors, prove that ′α′ is a root of the equation x^2 +4ax+2a^2 +6=0

$i f 3 x^{2} + 2 α x y + 2 y^{2} + 2 a x - 4 y + 1$ $c a n b e r e s o l v e d i n t o t w o l i n e a r$ $f a c t o r s, p r o v e t h a t^{'} α^{'} i s a r o o t$ $o f t h e e q u a t i o n x^{2} + 4 a x + 2 a^{2} + 6 = 0$

Question Number 37139 Answers: 2 Comments: 0

if α , β are the roots of the quadratic equation ax^2 +bx+c =0 then find the quadratic equation whose roots are α^(2 ) , β^2

$i f α, β a r e t h e r o o t s o f t h e q u a d r a t i c$ $e q u a t i o n {a x}^{2} + b x + c = 0 t h e n f i n d$ $t h e q u a d r a t i c e q u a t i o n w h o s e r o o t s$ $a r e α^{2}, β^{2}$

Question Number 36926 Answers: 1 Comments: 0

let f(x) = e^(−x^2 ) 1) prove that f^((n)) (x)=p_n (x)e^(−x^2 ) with p_n is a polynom 2) find a relation of recurrence between the p_n 3) calculate p_1 ,p_2 ,p_3 ,p_4

$l e t f (x) = e^{- x^{2}}$ $1) p r o v e t h a t f^{(n)} (x) = p_{n} (x) e^{- x^{2}} w i t h p_{n} i s a p o l y n o m$ $2) f i n d a r e l a t i o n o f r e c u r r e n c e b e t w e e n t h e p_{n}$ $3) c a l c u l a t e p_{1}, p_{2}, p_{3}, p_{4}$