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AlgebraQuestion and Answers: Page 86

Question Number 180856 Answers: 1 Comments: 0

find all values of m∈R such that the equation: ∫_0 ^( x) ((arctany)/y) dy = mx has two real roots: x_1 ∈(−∞;0) , x_2 ∈(0;∞)

$find all values of m \in R such that the equation :$ $\int_{0}^{x} \frac{\arctan y}{y} dy = mx$ $has two real roots : x_{1} \in (- \infty; 0), x_{2} \in (0; \infty)$

Question Number 180894 Answers: 3 Comments: 2

x^3 +x=1 x^8 +3x^3 =?

$x^{3} + x = 1$ $x^{8} + 3 x^{3} = ?$

Question Number 180800 Answers: 0 Comments: 0

Question Number 180785 Answers: 2 Comments: 0

solve (1−x−x^2 ...)(2−x−x^2 ...)

$s o l v e (1 - x - x^{2} . . .) (2 - x - x^{2} . . .)$

Question Number 180778 Answers: 0 Comments: 0

Question Number 180759 Answers: 1 Comments: 0

Find all functions f : R→R for all x, y ∈R such that f(f(x−y)−yf(x))=xf(y)

$F i n d a l l f u n c t i o n s f : R \to R f o r a l l x, y \in R s u c h t h a t$ $f (f (x - y) - y f (x)) = x f (y)$

Question Number 180728 Answers: 1 Comments: 0

Given x, y, z∈R^+ such that x^2 −3xy+4y^2 −z=0. when ((xy)/z) reaches its max value, find the max value of (2/x)+(1/y)−(2/z).

$Given x, y, z \in R^{+} such that x^{2} - 3 x y + 4 y^{2} - z = 0 .$ $when \frac{x y}{z} reaches its \max value, find the \max value of$ $\frac{2}{x} + \frac{1}{y} - \frac{2}{z} .$

Question Number 180744 Answers: 2 Comments: 2

Question Number 180604 Answers: 1 Comments: 0

Question Number 180603 Answers: 0 Comments: 1

find the real solution of following equation system: x^2 +xy+y^2 =p y^2 +yz+z^2 =q z^2 +zx+x^2 =r with p,q,r>0

$f i n d t h e r e a l s o l u t i o n o f f o l l o w i n g$ $e q u a t i o n s y s t e m :$ $x^{2} + x y + y^{2} = p$ $y^{2} + y z + z^{2} = q$ $z^{2} + z x + x^{2} = r$ $w i t h p, q, r > 0$

Question Number 180569 Answers: 1 Comments: 1

(√(x+4)) − (√(x−1)) > (√(4x+5))

$\sqrt{x + 4} - \sqrt{x - 1} > \sqrt{4 x + 5}$

Question Number 180565 Answers: 2 Comments: 1

(2x+(√(4x^2 +1)))(3y+(√(9y^2 +1)))=1 (4x+6y)^3 =? Show full solution

$(2 x + \sqrt{4 x^{2} + 1}) (3 y + \sqrt{9 y^{2} + 1}) = 1$ ${(4 x + 6 y)}^{3} = ?$ $S h o w f u l l s o l u t i o n$

Question Number 180550 Answers: 1 Comments: 0

Resoudre af^′ (x)+(b/(f(x)))+c=0 (a,b,c)∈R^3

$R e s o u d r e$ ${a f}^{^{'}} (x) + \frac{b}{f (x)} + c = 0 (a, b, c) \in R^{3}$

Question Number 180542 Answers: 2 Comments: 0

Resoudre dans R 1) a+b+c=2 a^2 +b^2 +c^2 =6 (1/a)+(1/b)+(1/c)=(1/2) 2) x^2 +xy+y^2 =3 y^2 +yz+z^2 =7 z^2 +zx+x^2 =13

$R e s o u d r e d a n s R$ $1)$ $a + b + c = 2$ $a^{2} + b^{2} + c^{2} = 6$ $\frac{1}{a} + \frac{1}{b} + \frac{1}{c} = \frac{1}{2}$ $2)$ $x^{2} + x y + y^{2} = 3$ $y^{2} + y z + z^{2} = 7$ $z^{2} + z x + x^{2} = 13$

Question Number 180652 Answers: 1 Comments: 0

Question Number 180653 Answers: 2 Comments: 0

Question Number 180490 Answers: 3 Comments: 0

Question Number 180483 Answers: 0 Comments: 1

Question Number 180407 Answers: 2 Comments: 0

f(x−y)+f(x+y)=f(x)f(y) find f(x)

$f (x - y) + f (x + y) = f (x) f (y)$ $find f (x)$

Question Number 180396 Answers: 0 Comments: 0

The difference between the ages of Sammy and Cindy is half the difference between the ages of their parents. Their father is 6 years older than twice the age of Cindy. Their mother is twice as old as Cindy and 12 years older than Sammy. By how many years is Sammy younger than Cindy?

$The difference between the ages of$ $Sammy and Cindy is half the$ $difference between the ages of$ $their parents . Their father is 6$ $years older than twice the age of$ $Cindy . Their mother is twice as old$ $as Cindy and 12 years older than$ $Sammy . By how many years is$ $Sammy younger than Cindy ?$

Question Number 180391 Answers: 1 Comments: 1

y = x − (2/x) Find the set of values of the function.

$y = x - \frac{2}{x}$ $Find the set of values of the function .$

Question Number 180381 Answers: 2 Comments: 0

(√((8^(12) +4^(13) )/(8^6 +4^(14) )))

$\sqrt{\frac{8^{12} + 4^{13}}{8^{6} + 4^{14}}}$

Question Number 180351 Answers: 0 Comments: 0

solve the differential equation y′′ +2 y′ + y = 0 using power series method that is, assume y = Σ_(n=0) ^∞ c_n x^n is a solution

$solve the differential equation y^{″} + 2 y^{'} + y = 0$ $using power series method that is, assume$ $y = \underset{n = 0}{\sum^{\infty}} c_{n} x^{n} is a solution$

Question Number 180348 Answers: 0 Comments: 0

Question Number 180274 Answers: 1 Comments: 0

Solve in C the equation z^4 +(7−i)z^3 +(12−15i)z^2 +(4+4i)z+16+192i=0 Knowing that it has one real root and a purely imaginary root of equal magnitude.

$Solve in C the equation$ $z^{4} + (7 - i) z^{3} + (12 - 15 i) z^{2} + (4 + 4 i) z + 16 + 192 i = 0$ $Knowing that it has one real root and a purely imaginary root$ $of equal magnitude .$

Question Number 180273 Answers: 0 Comments: 0

In triangle ABC with angles α , β , γ correspondently , Euler′s line interescts BC at point P. Ite′s put δ is angle between Euler′s line and BC (∠BPH). Then the following is true tan δ = ((2 cos β cos γ − cos α)/(sin (β − γ)))

$In triangle ABC with angles α, β, γ$ $correspondently, {Euler}^{'} s line interescts$ $BC at point P . {Ite}^{'} s put δ is angle$ $between {Euler}^{'} s line and BC (∠ BPH) .$ $Then the following is true$ $\tan δ = \frac{2 \cos β \cos γ - \cos α}{\sin (β - γ)}$

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