Question and Answers Forum

AlgebraQuestion and Answers: Page 302

Question Number 62844 Answers: 1 Comments: 0

Let p(x) = ax^2 + bx + c be such that p(x) takes real values for real values of x and non−real values for non−real values of x . Prove that a = 0 and find all possible values of c.

$${Let}\:{p}\left({x}\right)\:=\:{ax}^{\mathrm{2}} \:+\:{bx}\:+\:{c}\:\:{be}\:{such}\:{that}\:{p}\left({x}\right)\:{takes}\:{real}\:{values} \\ $$$${for}\:{real}\:{values}\:{of}\:{x}\:{and}\:{non}−{real}\:{values}\:{for}\:{non}−{real} \\ $$$${values}\:{of}\:{x}\:.\:{Prove}\:{that}\:{a}\:=\:\mathrm{0}\:{and}\:{find}\:{all} \\ $$$${possible}\:{values}\:{of}\:{c}. \\ $$

Question Number 62798 Answers: 0 Comments: 0

Calculate tg(20°)+4sin(20°)+1

$$\boldsymbol{\mathrm{Calculate}} \\ $$$$\boldsymbol{\mathrm{tg}}\left(\mathrm{20}°\right)+\mathrm{4}\boldsymbol{\mathrm{sin}}\left(\mathrm{20}°\right)+\mathrm{1} \\ $$

Question Number 62676 Answers: 1 Comments: 1

Question Number 62672 Answers: 1 Comments: 9

Question Number 62669 Answers: 2 Comments: 0

calculate the value of Σ_(n=0) ^(1947) (1/(2^n +(√2^(1947) )))

$${calculate}\:{the}\:{value}\:{of}\:\underset{{n}=\mathrm{0}} {\overset{\mathrm{1947}} {\sum}}\frac{\mathrm{1}}{\mathrm{2}^{{n}} +\sqrt{\mathrm{2}^{\mathrm{1947}} }} \\ $$

Question Number 62623 Answers: 0 Comments: 0

Question Number 62577 Answers: 1 Comments: 1

Question Number 62494 Answers: 0 Comments: 0

Question Number 62489 Answers: 3 Comments: 0

solve for x: (((√(2 − x)) + (√(2 + x)))/((√(2 − x)) − (√(2 + x)))) = 3

$$\mathrm{solve}\:\mathrm{for}\:\mathrm{x}:\:\:\:\:\:\:\:\frac{\sqrt{\mathrm{2}\:−\:\mathrm{x}}\:+\:\sqrt{\mathrm{2}\:+\:\mathrm{x}}}{\sqrt{\mathrm{2}\:−\:\mathrm{x}}\:−\:\sqrt{\mathrm{2}\:+\:\mathrm{x}}}\:\:=\:\:\mathrm{3} \\ $$

Question Number 62468 Answers: 1 Comments: 1

Question Number 62452 Answers: 1 Comments: 0

Find the remainder when 2014! is divisible by 2017

$$\mathrm{Find}\:\mathrm{the}\:\mathrm{remainder}\:\mathrm{when}\:\:\:\mathrm{2014}!\:\:\mathrm{is}\:\mathrm{divisible}\:\mathrm{by}\:\:\mathrm{2017} \\ $$

Question Number 62449 Answers: 2 Comments: 1

Find the number of digit in 2^(50)

$$\mathrm{Find}\:\mathrm{the}\:\mathrm{number}\:\mathrm{of}\:\mathrm{digit}\:\mathrm{in}\:\:\:\:\mathrm{2}^{\mathrm{50}} \\ $$

Question Number 62439 Answers: 0 Comments: 1

sove inside Z/3Z the systeme { ((5x+7y =10)),((2x+5y =8)) :}

$${sove}\:{inside}\:{Z}/\mathrm{3}{Z}\:{the}\:{systeme} \\ $$$$\begin{cases}{\mathrm{5}{x}+\mathrm{7}{y}\:=\mathrm{10}}\\{\mathrm{2}{x}+\mathrm{5}{y}\:=\mathrm{8}}\end{cases} \\ $$$$ \\ $$

Question Number 62428 Answers: 0 Comments: 6

Question Number 62424 Answers: 1 Comments: 2

Question Number 62396 Answers: 0 Comments: 0

Question Number 62372 Answers: 1 Comments: 0

Solve for x , y 3x>2y ∧ 2x<3y where x,y∈N

$${Solve}\:{for}\:{x}\:,\:{y} \\ $$$$\mathrm{3}{x}>\mathrm{2}{y}\:\wedge\:\mathrm{2}{x}<\mathrm{3}{y}\: \\ $$$${where}\:{x},{y}\in\mathbb{N} \\ $$

Question Number 62334 Answers: 2 Comments: 0

if α^2 +β^2 = (α+β)^2 −2αβ evaluate(α−β)

$${if}\:\alpha^{\mathrm{2}} +\beta^{\mathrm{2}} =\:\left(\alpha+\beta\right)^{\mathrm{2}} −\mathrm{2}\alpha\beta\:{evaluate}\left(\alpha−\beta\right) \\ $$

Question Number 62281 Answers: 1 Comments: 0

{ ((x^3 +y^3 =3xy)),((x^4 +y^4 =4xy)) :} [x,y≠0]

$$\begin{cases}{\boldsymbol{\mathrm{x}}^{\mathrm{3}} +\boldsymbol{\mathrm{y}}^{\mathrm{3}} =\mathrm{3}\boldsymbol{\mathrm{xy}}}\\{\boldsymbol{\mathrm{x}}^{\mathrm{4}} +\boldsymbol{\mathrm{y}}^{\mathrm{4}} =\mathrm{4}\boldsymbol{\mathrm{xy}}}\end{cases}\:\:\:\:\:\:\:\:\:\:\:\:\:\:\left[\boldsymbol{\mathrm{x}},\boldsymbol{\mathrm{y}}\neq\mathrm{0}\right] \\ $$

Question Number 62276 Answers: 1 Comments: 0

{ ((((√x)/a)+((√y)/b)=1)),((((√a)/x)+((√b)/y)=1)) :} a,b∈R^+

$$\begin{cases}{\frac{\sqrt{\boldsymbol{\mathrm{x}}}}{\boldsymbol{\mathrm{a}}}+\frac{\sqrt{\boldsymbol{\mathrm{y}}}}{\boldsymbol{\mathrm{b}}}=\mathrm{1}}\\{\frac{\sqrt{\boldsymbol{\mathrm{a}}}}{\boldsymbol{\mathrm{x}}}+\frac{\sqrt{\boldsymbol{\mathrm{b}}}}{\boldsymbol{\mathrm{y}}}=\mathrm{1}}\end{cases}\:\:\:\boldsymbol{\mathrm{a}},\boldsymbol{\mathrm{b}}\in\mathrm{R}^{+} \\ $$

Question Number 62275 Answers: 1 Comments: 0

{ ((a(√x)+b(√y)=2(√(ab)))),((x(√a)+y(√b)=2(√(ab)))) :} a,b∈R^+

$$\begin{cases}{\boldsymbol{\mathrm{a}}\sqrt{\boldsymbol{\mathrm{x}}}+\boldsymbol{\mathrm{b}}\sqrt{\boldsymbol{\mathrm{y}}}=\mathrm{2}\sqrt{\boldsymbol{\mathrm{ab}}}}\\{\boldsymbol{\mathrm{x}}\sqrt{\boldsymbol{\mathrm{a}}}+\boldsymbol{\mathrm{y}}\sqrt{\boldsymbol{\mathrm{b}}}=\mathrm{2}\sqrt{\boldsymbol{\mathrm{ab}}}}\end{cases}\:\:\:\:\:\:\boldsymbol{\mathrm{a}},\boldsymbol{\mathrm{b}}\in\mathrm{R}^{+} \\ $$

Question Number 62234 Answers: 1 Comments: 0

Question Number 62228 Answers: 0 Comments: 2

{ (((√(a+x))+(√(a−y))=2a)),(((√(a−x))+(√(a+y))=2a)) :} a∈R.

$$\begin{cases}{\sqrt{\boldsymbol{\mathrm{a}}+\boldsymbol{\mathrm{x}}}+\sqrt{\boldsymbol{\mathrm{a}}−\boldsymbol{\mathrm{y}}}=\mathrm{2}\boldsymbol{\mathrm{a}}}\\{\sqrt{\boldsymbol{\mathrm{a}}−\boldsymbol{\mathrm{x}}}+\sqrt{\boldsymbol{\mathrm{a}}+\boldsymbol{\mathrm{y}}}=\mathrm{2}\boldsymbol{\mathrm{a}}}\end{cases}\:\:\:\:\:\boldsymbol{\mathrm{a}}\in\boldsymbol{\mathrm{R}}. \\ $$

Question Number 62211 Answers: 0 Comments: 3

(x/((√(4−x^2 ))+3))Max=(5/3)?

$$\frac{{x}}{\sqrt{\mathrm{4}−{x}^{\mathrm{2}} }+\mathrm{3}}{Max}=\frac{\mathrm{5}}{\mathrm{3}}? \\ $$

Question Number 62184 Answers: 0 Comments: 1

((2x−1))^(1/3) + (√(3x+1)) = 3(x)^(1/4)

$$\sqrt[{\mathrm{3}}]{\mathrm{2}{x}−\mathrm{1}}\:+\:\sqrt{\mathrm{3}{x}+\mathrm{1}}\:=\:\mathrm{3}\sqrt[{\mathrm{4}}]{{x}} \\ $$

Question Number 62176 Answers: 2 Comments: 0

Pg 297 Pg 298 Pg 299 Pg 300 Pg 301 Pg 302 Pg 303 Pg 304 Pg 305 Pg 306

Contact: info@tinkutara.com