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AlgebraQuestion and Answers: Page 54

Question Number 196582 Answers: 1 Comments: 0

If x = log_a bc, y = log_b ca and z = log_c ab then prove that x + y + z = xyz − 2.

$If x = \log_{a} b c, y = \log_{b} c a and z = \log_{c} a b$ $then prove that x + y + z = x y z - 2 .$

Question Number 196555 Answers: 0 Comments: 0

In △ABC show that Σ ((1 + cos ∙ (A − B) ∙ cos C)/(h_C ∙ sec C)) = (3/(2 R))

$In △ ABC show that$ $Σ \frac{1 + \cos \cdot (A - B) \cdot \cos C}{h_{C} \cdot \sec C} = \frac{3}{2 R}$

Question Number 196614 Answers: 2 Comments: 0

if S_n =(1/(1+5n))+(1/(2+5n))+(1/(3+5n))+...+(1/(6n)), find lim_(n→∞) S_n =?

$i f S_{n} = \frac{1}{1 + 5 n} + \frac{1}{2 + 5 n} + \frac{1}{3 + 5 n} + . . . + \frac{1}{6 n},$ $f i n d \lim_{n \to \infty} S_{n} = ?$

Question Number 196612 Answers: 0 Comments: 1

Question Number 196544 Answers: 1 Comments: 0

Question Number 196519 Answers: 1 Comments: 0

if xyz=1, prove ((x/(x−1)))^2 +((y/(y−1)))^2 +((z/(z−1)))^2 ≥1.

$i f x y z = 1, p r o v e$ ${(\frac{x}{x - 1})}^{2} + {(\frac{y}{y - 1})}^{2} + {(\frac{z}{z - 1})}^{2} ⩾ 1 .$

Question Number 196515 Answers: 1 Comments: 0

Find: ∫_0 ^( +∞) x^𝛑 e^(−x) dx = ?

$Find : \int_{0}^{+ \infty} x^{π} e^{- x} dx = ?$

Question Number 196483 Answers: 0 Comments: 0

Question Number 196450 Answers: 3 Comments: 0

one solution of the equation (x−a)(x−b)(x−c)(x−d) = 9 is x=2. If a,b,c,d are different integers then a+b+c+d =?

$one solution of the equation$ $(x - a) (x - b) (x - c) (x - d) = 9$ $is x = 2 . If a, b, c, d are different$ $integers then a + b + c + d = ?$

Question Number 196364 Answers: 1 Comments: 0

xp(x)=x^3 −2x^2 +x−a p(−1)=?

$x p (x) = x^{3} - 2 x^{2} + x - a$ $p (- 1) = ?$

Question Number 196360 Answers: 2 Comments: 1

Question Number 196355 Answers: 2 Comments: 1

log_5 (√(5(√(5(√(5(√(5.....)))))) ))= ?

$\log_{5} \sqrt{5 \sqrt{5 \sqrt{5 \sqrt{5 . . . . .}}}} = ?$

Question Number 196358 Answers: 0 Comments: 2

Question Number 196343 Answers: 2 Comments: 0

find the minimum value of f(x) f(x) = (√(x^2 −2x +5)) + (√(4x^2 −4x +10 ))

$find the minimum value of f (x)$ $f (x) = \sqrt{x^{2} - 2 x + 5} + \sqrt{{4 x}^{2} - 4 x + 10}$

Question Number 196325 Answers: 1 Comments: 0

Σ_(n=0) ^∞ arg(n^2 +n+1+i)= π/2

$\underset{n = 0}{\sum^{\infty}} a r g (n^{2} + n + 1 + i) = π / 2$

Question Number 196300 Answers: 2 Comments: 0

If → n ∈ N and n ≥ 2 Then → tan ((1/(n − 1)) Σ_(k=2) ^n arctan (1/k)) < (2/5) + (𝛄/(n − 1))

$If \to n \in N and n ⩾ 2$ $Then \to \tan (\frac{1}{n - 1} \underset{k = 2}{\sum^{n}} \arctan \frac{1}{k}) < \frac{2}{5} + \frac{γ}{n - 1}$

Question Number 196299 Answers: 1 Comments: 0

If → y = x ! find → (dy/dx)

$If \to y = x! find \to \frac{dy}{dx}$

Question Number 196288 Answers: 3 Comments: 1

4^x =(√5^y )=400 ((xy)/(2x+y))=?

$4^{x} = \sqrt{5^{y}} = 400$ $\frac{x y}{2 x + y} = ?$

Question Number 196285 Answers: 0 Comments: 1

problem 196258 (please)

$p r o b l e m 196258 (p l e a s e)$

Question Number 196185 Answers: 1 Comments: 0

$\underset{⏟}{}$

Question Number 196183 Answers: 2 Comments: 0

Question Number 196165 Answers: 3 Comments: 0

{: ((x^(x+y) =y^(24) )),((y^(x+y) =x^6 )) }⇒(x,y)=(?,?)

$\begin{matrix} x^{x + y} = y^{24} \\ y^{x + y} = x^{6} \end{matrix}} \Rightarrow (x, y) = (?, ?)$

Question Number 196121 Answers: 0 Comments: 0

In forest , a hunter obstains that Every morning a snake eats a mouse Every afternoon a scorpion kills a snake Every night a mouse corrodes a scorpion The 8^(th) day morning , there remains Only one of them , a mouse How many were they, in each species?

$I n f o r e s t, a h u n t e r o b s t a i n s t h a t$ $E v e r y m o r n i n g a s n a k e e a t s a m o u s e$ $E v e r y a f t e r n o o n a s c o r p i o n k i l l s a s n a k e$ $E v e r y n i g h t a m o u s e c o r r o d e s a s c o r p i o n$ $T h e 8^{t h} d a y m o r n i n g, t h e r e r e m a i n s$ $O n l y o n e o f t h e m, a m o u s e$ $H o w m a n y w e r e t h e y, i n e a c h s p e c i e s ?$

Question Number 196119 Answers: 5 Comments: 0

solve (√(100−x^2 ))+(√(64−x^2 ))=12

$s o l v e$ $\sqrt{100 - x^{2}} + \sqrt{64 - x^{2}} = 12$

Question Number 196102 Answers: 0 Comments: 0

Question Number 196086 Answers: 0 Comments: 0

Answer to the question “196008” Σ_(k=1) ^n tan^2 (((kπ)/(2n+1)))=n(2n+1) Ans) according “de moivre” sin(2n+1)α= (((2n+1)),(( 1)) )(cosα)^(2n) sinα− (((2n+1)),(( 3)) )(cosα)^(2n−2) (sinα)^3 +.... =(cosα)^(2n) (sinα)[ (((2n+1)),(( 1)) )− (((2n+1)),(( 3)) ) tan^2 α+...] for “α_k =((kπ)/(2n+1)) ; 1≤k≤n ⇒sin(2n+1)α_k =0 ⇒∀ 1≤k≤n→ (((2n+1)),(( 1)) )− (((2n+1)),(( 3)) ) tan^2 α_k +...=0 therefore “ x_k =tan^2 α_k ” thr roots of the equation are blowe x^n − (((2n+1)),((2n−1)) ) x^n + (((2n+1)),((2n−3)) )x^(n−1) −...=0 the sume of the roots of the equation is “ s= (((2n+1)),((2n−1)) ) ” ⇒s=Σ_(k=1) ^n tan^2 (((kπ)/(2n+1)))=n(2n+1)✓ the proof of the seconf part is done similarly

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