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AllQuestion and Answers: Page 146

Question Number 201912 Answers: 0 Comments: 2

Question Number 201907 Answers: 1 Comments: 0

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Question Number 201877 Answers: 0 Comments: 0

Question Number 201873 Answers: 1 Comments: 0

Question Number 201864 Answers: 0 Comments: 2

(ct^2 −(1/(ct^2 ))+(√2))^2 =c^2 (t^4 +(1/t^4 )) Find t=f(c).

${({c t}^{2} - \frac{1}{{c t}^{2}} + \sqrt{2})}^{2} = c^{2} (t^{4} + \frac{1}{t^{4}})$ $F i n d t = f (c) .$

Question Number 201860 Answers: 1 Comments: 0

𝚺_(n=1) ^∞ (((−1)^n H_n )/(n+1))=??

$\underset{n = 1}{\sum^{\infty}} \frac{{(- 1)}^{n} H_{n}}{n + 1} = ? ?$

Question Number 201859 Answers: 0 Comments: 0

If xyz ∈R^+ , xyz=1 , prove that the following inequality holds: (x/(2x^5 +x+4))+(y/(2y^5 +y+4))+(z/(2z^5 +z+4))≥(3/7). Solution please with an advice to get better at inequalities and which book would you recommend. Thanks in advance!

$If x y z \in R^{+}, x y z = 1, prove that the following inequality holds :$ $\frac{x}{2 x^{5} + x + 4} + \frac{y}{2 y^{5} + y + 4} + \frac{z}{2 z^{5} + z + 4} ⩾ \frac{3}{7} .$ $Solution please with an advice to get better$ $at inequalities and which book would you recommend .$ $Thanks in advance!$

Question Number 201857 Answers: 1 Comments: 1

If a,b,c,d,e are thr roots of 2x^5 −3x^3 +2x−7=0 , find the value of Π_(cyc) (a^3 −1)

$If a, b, c, d, e are thr roots of$ ${2 x}^{5} - {3 x}^{3} + 2 x - 7 = 0, find the$ $value of \prod_{cyc} (a^{3} - 1)$

Question Number 201854 Answers: 0 Comments: 3

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Question Number 201850 Answers: 0 Comments: 0

Question Number 201897 Answers: 0 Comments: 0

Question: The congruence equation ′′ ( 5a +3 )x ≡^(3a + 4) 19 ′′ is given. Find the sum of digits of the smallest three −digit natural number ” a ” such that the assumed equation has no solution in ” Z ”.

$Q u e s t i o n : T h e c o n g r u e n c e$ $e q u a t i o n^{″} (5 a + 3) x \overset{3 a + 4}{\equiv} 19^{″} i s g i v e n .$ $F i n d t h e s u m o f d i g i t s o f$ $t h e s m a l l e s t t h r e e - d i g i t n a t u r a l n u m b e r^{″} a^{″}$ $s u c h t h a t t h e a s s u m e d e q u a t i o n h a s$ $n o s o l u t i o n i n^{″} Z^{″} .$

Question Number 201848 Answers: 1 Comments: 0

Question Number 201846 Answers: 0 Comments: 1

Question Number 201839 Answers: 0 Comments: 1

Question Number 201837 Answers: 0 Comments: 0

y′′′−y′′+y′=sec(t),−(π/2)<t<(π/2)

$y^{‴} - y^{″} + y^{'} = s e c (t), - \frac{π}{2} < t < \frac{π}{2}$

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