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Question Number 156462 Answers: 1 Comments: 0

If abc^(−) = cba^(−) + def^(−) and a∈{c+2;...;9} Then find def^(−) + fed^(−)

$If \overset{―}{abc} = \overset{―}{cba} + \overset{―}{def} and a \in {c + 2; . . .; 9}$ $Then find \overset{―}{def} + \overset{―}{fed}$

Question Number 156482 Answers: 1 Comments: 0

Solve for real numbers: 3 + sin(2x) = 4sin(x + (π/4))

$Solve for real numbers :$ $3 + \sin (2 x) = 4 \sin (x + \frac{π}{4})$

Question Number 156573 Answers: 0 Comments: 0

if a;b;c;d>1 then: Σ_(cyc) log_a (((b^3 + c^3 + d^3 )/(b^2 + c^2 + d^2 ))) ≥ 4

$if a; b; c; d > 1 then :$ $\sum_{cyc} \log_{a} (\frac{b^{3} + c^{3} + d^{3}}{b^{2} + c^{2} + d^{2}}) ⩾ 4$

Question Number 156571 Answers: 1 Comments: 0

Question Number 156458 Answers: 0 Comments: 0

Question Number 156455 Answers: 1 Comments: 4

Question Number 156453 Answers: 0 Comments: 0

Solve for real numbers: 9 + log_2 (x/(x^4 + 48)) = 2 + (2/( (√(x - 1))))

$Solve for real numbers :$ $9 + \log_{2} \frac{x}{x^{4} + 48} = 2 + \frac{2}{\sqrt{x - 1}}$

Question Number 156452 Answers: 0 Comments: 0

Find x;y;z≥0 such that: { ((x-y-z = sinx-siny-sinz)),((x^2 -y^2 -z^2 = sin^2 x-sin^2 y-sin^2 z)),((x^3 -y^3 -z^3 = sin^3 x-sin^3 y-sin^3 z)) :}

$Find x; y; z ⩾ 0 such that :$ ${\begin{cases} x - y - z = \sin x - \sin y - \sin z \\ x^{2} - y^{2} - z^{2} = \sin^{2} x - \sin^{2} y - \sin^{2} z \\ x^{3} - y^{3} - z^{3} = \sin^{3} x - \sin^{3} y - \sin^{3} z \end{cases}$

Question Number 156450 Answers: 0 Comments: 2

Question Number 156448 Answers: 1 Comments: 0

If 0<a≤b<π then prove that: ((sin(√(ab)))/(sin(((a+b)/2)))) ≥ ((32a^2 b^2 (√(ab)))/((a+b)^5 ))

$If 0 < a ⩽ b < π then prove that :$ $\frac{\sin \sqrt{ab}}{\sin (\frac{a + b}{2})} ⩾ \frac{{32 a}^{2} b^{2} \sqrt{ab}}{{(a + b)}^{5}}$

Question Number 156447 Answers: 1 Comments: 0

Find all functions f : Z → R such that f(n+m)=nf(n)+mf(m)+nm-n-m ∀n;m∈Z

$Find all functions f : Z \to R such that$ $f (n + m) = nf (n) + mf (m) + nm - n - m$ $\forall n; m \in Z$

Question Number 156434 Answers: 0 Comments: 0

Question Number 156432 Answers: 0 Comments: 0

in a second order differenti equation, a 4 henry inductor,an 8 ohm resistor and o.2 farad capacito are connected in series with the temperature of the battery with ggl. E=80 sin 3t. solid=0 the charge in the capacitor and the current in the circuit is zero. a.charge b.current at t>0

$in a second order differenti equation, a 4 henry$ $inductor, an 8 ohm resistor and o . 2 farad capacito$ $are connected in series with the temperature of$ $the battery with ggl . E = 80 \sin 3 t . solid = 0 the$ $charge in the capacitor and the current in the$ $circuit is zero .$ $a . charge$ $b . current at t > 0$

Question Number 156426 Answers: 1 Comments: 0

Given that tan α and tan β are the roots of the equation x^2 +3ax+4a+1=0, where a>1 and α,β∈(−(π/2),(π/2)). Evaluate tan(((α+β)/2)).

$Given that \tan α and \tan β are the roots$ $of the equation x^{2} + 3 a x + 4 a + 1 = 0,$ $where a > 1 and α, β \in (- \frac{π}{2}, \frac{π}{2}) .$ $Evaluate \tan (\frac{α + β}{2}) .$

Question Number 156423 Answers: 1 Comments: 2

Question Number 156422 Answers: 1 Comments: 2

Question Number 156421 Answers: 0 Comments: 2

Question Number 156419 Answers: 1 Comments: 1

x is positive integer number can you check if Q=((((x+2)^4 −x^4 ))^(1/3) is a natural number

$x is positive integer number$ $can you check if Q = \sqrt[3]{({(x + 2)}^{4} - x^{4}}$ $is a natural number$

Question Number 156413 Answers: 2 Comments: 0

Question Number 156404 Answers: 0 Comments: 3

x^4 +bx^2 +cx+d=0 let cx=m+px^2 +x^4 ⇒ 2x^4 +(b+p)x^2 +m+d=0 x^2 =−(((b+p)/4))±(√((((b+p)/4))^2 −(((m+d)/2)))) (p−b)x^2 −2cx+m−d=0 x=(c/(p−b))±(√(((c/(p−b)))^2 −(((m−d)/(p−b))))) ⇒ (((b^2 −p^2 ))/4)±(√(((b^2 −p^2 )^2 −8(p−b)^2 (m+d))/(16))) +((2c^2 )/(b−p))∓(√((4c^4 −4c^2 (p−b)(m−d))/((p−b)^2 ))) +m−d=0 Just if m=d ⇒ (((b^2 −p^2 ))/4)±(√(((b^2 −p^2 )^2 −16d(p−b))/(16))) +((4c^2 )/(b−p))=0 ⇒ (((b^2 −p^2 )/4)+((4c^2 )/(b−p)))^2 +d(p−b)=(((b^2 −p^2 )^2 )/(16)) ⇒ ((16c^4 )/((b−p)^2 ))+(d+2c^2 )(b+p)=0 let b−p=z z^2 (2b−z)=−((16c^4 )/(2c^2 +d)) z^3 −2bz^2 −k=0 (k>0) if b=−1 , d=0, c→−c z^3 +2z^2 −8c^2 =0 let z=((2c)/t) 8c^3 +8c^2 t−8c^2 t^3 =0 ⇒ t^3 −t=c back to square one.

$x^{4} + {bx}^{2} + cx + d = 0$ $let cx = m + {px}^{2} + x^{4}$ $\Rightarrow {2 x}^{4} + (b + p) x^{2} + m + d = 0$ $x^{2} = - (\frac{b + p}{4}) \pm \sqrt{{(\frac{b + p}{4})}^{2} - (\frac{m + d}{2})}$ $(p - b) x^{2} - 2 cx + m - d = 0$ $x = \frac{c}{p - b} \pm \sqrt{{(\frac{c}{p - b})}^{2} - (\frac{m - d}{p - b})}$ $\Rightarrow$ $\frac{(b^{2} - p^{2})}{4} \pm \sqrt{\frac{{(b^{2} - p^{2})}^{2} - 8 {(p - b)}^{2} (m + d)}{16}}$ $+ \frac{{2 c}^{2}}{b - p} \mp \sqrt{\frac{{4 c}^{4} - {4 c}^{2} (p - b) (m - d)}{{(p - b)}^{2}}}$ $+ m - d = 0$ $J u s t i f m = d \Rightarrow$ $\frac{(b^{2} - p^{2})}{4} \pm \sqrt{\frac{{(b^{2} - p^{2})}^{2} - 16 d (p - b)}{16}}$ $+ \frac{{4 c}^{2}}{b - p} = 0$ $\Rightarrow$ ${(\frac{b^{2} - p^{2}}{4} + \frac{{4 c}^{2}}{b - p})}^{2} + d (p - b) = \frac{{(b^{2} - p^{2})}^{2}}{16}$ $\Rightarrow \frac{{16 c}^{4}}{{(b - p)}^{2}} + (d + {2 c}^{2}) (b + p) = 0$ $let b - p = z$ $z^{2} (2 b - z) = - \frac{{16 c}^{4}}{{2 c}^{2} + d}$ $z^{3} - {2 bz}^{2} - k = 0 (k > 0)$ $if b = - 1, d = 0, c \to - c$ $z^{3} + {2 z}^{2} - {8 c}^{2} = 0$ $let z = \frac{2 c}{t}$ ${8 c}^{3} + {8 c}^{2} t - {8 c}^{2} t^{3} = 0$ $\Rightarrow t^{3} - t = c$ $back to square one .$

Question Number 156403 Answers: 0 Comments: 1

find two numbers between (1/3)and (3/4)

$find two numbers between$ $\frac{1}{3} and \frac{3}{4}$

Question Number 156400 Answers: 0 Comments: 1

Question Number 156384 Answers: 0 Comments: 0

Question Number 156381 Answers: 0 Comments: 1

∫_0 ^( (𝛑/2)) (x^2 /(sin(x))) dx

$\int_{0}^{\frac{π}{2}} \frac{x^{2}}{s i n (x)} d x$

Question Number 156386 Answers: 1 Comments: 0

φ (n )= Σ_(k=1) ^n (−1 )^( k−1) ((( n)),(( k)) ) H_( k) Find the value of : Σ_(n=1) ^∞ (−1)^( n−1) φ ( n^( 2) ) =?

$ϕ (n) = \underset{k = 1}{\sum^{n}} {(- 1)}^{k - 1} (\begin{matrix} n \\ k \end{matrix}) H_{k}$ $Find the value of :$ $\underset{n = 1}{\sum^{\infty}} {(- 1)}^{n - 1} ϕ (n^{2}) = ?$

Question Number 156373 Answers: 1 Comments: 0

A. lim_(x→+∞) Σ_(k=1) ^n [tan((kπ)/(2n))]

$A . \lim_{x \to + \infty} \underset{k = 1}{\sum^{n}} [\tan \frac{k π}{2 n}]$

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