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AlgebraQuestion and Answers: Page 356

Question Number 11753 Answers: 2 Comments: 0

a, b, c are the roots from equation x^3 − 5x^2 − 9x + 10 = 0 If P(x) = Ax^3 + Bx^2 + Cx − 2015 and P(a) = b + c P(b) = a + c P(c) = a + b What is the value of A + B + C ?

$${a},\:{b},\:{c}\:\mathrm{are}\:\mathrm{the}\:\mathrm{roots}\:\mathrm{from}\:\mathrm{equation}\:{x}^{\mathrm{3}} \:−\:\mathrm{5}{x}^{\mathrm{2}} \:−\:\mathrm{9}{x}\:+\:\mathrm{10}\:=\:\mathrm{0} \\ $$$$\mathrm{If}\:{P}\left({x}\right)\:=\:{Ax}^{\mathrm{3}} \:+\:{Bx}^{\mathrm{2}} \:+\:{Cx}\:−\:\mathrm{2015}\:\mathrm{and} \\ $$$${P}\left({a}\right)\:=\:{b}\:+\:{c}\: \\ $$$${P}\left({b}\right)\:=\:{a}\:+\:{c} \\ $$$${P}\left({c}\right)\:=\:{a}\:+\:{b} \\ $$$$\mathrm{What}\:\mathrm{is}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:{A}\:+\:{B}\:+\:{C}\:? \\ $$

Question Number 11748 Answers: 1 Comments: 0

Solve simultaneously x^2 + 4y^2 + xy = 6 .............. equation (i) 3x^2 + 8y^2 = 14 .............. equation (ii)

$$\mathrm{Solve}\:\mathrm{simultaneously} \\ $$$$\mathrm{x}^{\mathrm{2}} \:+\:\mathrm{4y}^{\mathrm{2}} \:+\:\mathrm{xy}\:=\:\mathrm{6}\:\:\:\:\:..............\:\mathrm{equation}\:\left(\mathrm{i}\right) \\ $$$$\mathrm{3x}^{\mathrm{2}} \:+\:\mathrm{8y}^{\mathrm{2}} \:=\:\mathrm{14}\:\:\:\:\:\:\:\:\:\:\:..............\:\mathrm{equation}\:\left(\mathrm{ii}\right) \\ $$

Question Number 11741 Answers: 1 Comments: 0

∫xtan^2 x dx=?

$$\int\mathrm{xtan}^{\mathrm{2}} \:\mathrm{x}\:\mathrm{dx}=? \\ $$

Question Number 11714 Answers: 0 Comments: 3

Solve the Crazy equation... x(lnx)^2 +xlnx−1=0

$${Solve}\:{the}\:{Crazy}\:{equation}... \\ $$$${x}\left({lnx}\right)^{\mathrm{2}} +{xlnx}−\mathrm{1}=\mathrm{0} \\ $$

Question Number 11707 Answers: 0 Comments: 0

ax^3 +bx^2 +cx+d=0 pls. solve it in a alzebric way , that a O level(ssc) student can understand...

$$ \\ $$$$ \\ $$$${ax}^{\mathrm{3}} +{bx}^{\mathrm{2}} +{cx}+{d}=\mathrm{0} \\ $$$${pls}.\:{solve}\:{it}\:{in}\:{a}\:{alzebric}\:{way}\:, \\ $$$${that}\:{a}\:{O}\:{level}\left({ssc}\right)\:{student}\:{can} \\ $$$${understand}... \\ $$$$ \\ $$

Question Number 11672 Answers: 2 Comments: 3

8x^3 −6x+1=0 Solves...

$$\mathrm{8}\boldsymbol{\mathrm{x}}^{\mathrm{3}} −\mathrm{6}\boldsymbol{\mathrm{x}}+\mathrm{1}=\mathrm{0} \\ $$$$\boldsymbol{\mathrm{Solves}}... \\ $$

Question Number 11661 Answers: 1 Comments: 0

8x^3 −6x+1=0. Solves... equation x_1 =? x_2 =?

$$\mathrm{8}\boldsymbol{\mathrm{x}}^{\mathrm{3}} −\mathrm{6}\boldsymbol{\mathrm{x}}+\mathrm{1}=\mathrm{0}. \\ $$$$\boldsymbol{\mathrm{Solves}}...\:\:\boldsymbol{\mathrm{equation}} \\ $$$$\boldsymbol{\mathrm{x}}_{\mathrm{1}} =?\:\:\:\:\:\boldsymbol{\mathrm{x}}_{\mathrm{2}} =? \\ $$

Question Number 11648 Answers: 1 Comments: 0

∣x∣<l Σ_(n=1) ^∞ x^n =?

$$\mid\mathrm{x}\mid<\mathrm{l} \\ $$$$\underset{\mathrm{n}=\mathrm{1}} {\overset{\infty} {\sum}}\mathrm{x}^{\mathrm{n}} =? \\ $$

Question Number 11628 Answers: 1 Comments: 0

p(x−1)+p(x+1)=4x^2 −2x+10 p(x)=?

$$\mathrm{p}\left(\mathrm{x}−\mathrm{1}\right)+\mathrm{p}\left(\mathrm{x}+\mathrm{1}\right)=\mathrm{4x}^{\mathrm{2}} −\mathrm{2x}+\mathrm{10} \\ $$$$\mathrm{p}\left(\mathrm{x}\right)=? \\ $$

Question Number 11543 Answers: 2 Comments: 0

solve for x and y in this equation x^x +y^y =31 x+y=5

$${solve}\:{for}\:{x}\:{and}\:{y}\:{in}\:{this}\:{equation} \\ $$$${x}^{{x}} +{y}^{{y}} =\mathrm{31} \\ $$$${x}+{y}=\mathrm{5} \\ $$

Question Number 11515 Answers: 2 Comments: 0

(((4+x)/x))^(1/5) −(((4−6x)/x))^(1/5) =1. x_1 +x_2 =?

$$\sqrt[{\mathrm{5}}]{\frac{\mathrm{4}+\boldsymbol{\mathrm{x}}}{\boldsymbol{\mathrm{x}}}}−\sqrt[{\mathrm{5}}]{\frac{\mathrm{4}−\mathrm{6}\boldsymbol{\mathrm{x}}}{\boldsymbol{\mathrm{x}}}}=\mathrm{1}. \\ $$$$\boldsymbol{\mathrm{x}}_{\mathrm{1}} +\boldsymbol{\mathrm{x}}_{\mathrm{2}} =? \\ $$

Question Number 11501 Answers: 3 Comments: 1

(4x^2 −7x−5)(5x^2 +13x+3)(3x−x^2 −8)=0. find all the multiples of the real roots of the equation.

$$\left(\mathrm{4}\boldsymbol{\mathrm{x}}^{\mathrm{2}} −\mathrm{7}\boldsymbol{\mathrm{x}}−\mathrm{5}\right)\left(\mathrm{5}\boldsymbol{\mathrm{x}}^{\mathrm{2}} +\mathrm{13}\boldsymbol{\mathrm{x}}+\mathrm{3}\right)\left(\mathrm{3}\boldsymbol{\mathrm{x}}−\boldsymbol{\mathrm{x}}^{\mathrm{2}} −\mathrm{8}\right)=\mathrm{0}. \\ $$$$\boldsymbol{\mathrm{find}}\:\:\boldsymbol{\mathrm{all}}\:\:\boldsymbol{\mathrm{the}}\:\:\boldsymbol{\mathrm{multiples}}\:\:\boldsymbol{\mathrm{of}}\:\:\boldsymbol{\mathrm{the}} \\ $$$$\boldsymbol{\mathrm{real}}\:\:\boldsymbol{\mathrm{roots}}\:\:\boldsymbol{\mathrm{of}}\:\:\boldsymbol{\mathrm{the}}\:\:\boldsymbol{\mathrm{equation}}. \\ $$

Question Number 11500 Answers: 2 Comments: 0

(x^2 +x−4)(x^2 +x+4)=9 find the equation has multiple roots.

$$\left(\boldsymbol{\mathrm{x}}^{\mathrm{2}} +\boldsymbol{\mathrm{x}}−\mathrm{4}\right)\left(\boldsymbol{\mathrm{x}}^{\mathrm{2}} +\boldsymbol{\mathrm{x}}+\mathrm{4}\right)=\mathrm{9} \\ $$$$\boldsymbol{\mathrm{find}}\:\:\boldsymbol{\mathrm{the}}\:\:\boldsymbol{\mathrm{equation}}\:\:\boldsymbol{\mathrm{has}}\:\:\boldsymbol{\mathrm{multiple}}\:\:\boldsymbol{\mathrm{roots}}. \\ $$

Question Number 11477 Answers: 2 Comments: 0

((a^8 +a^4 +1)/(a^6 +1)). solves....

$$\frac{\boldsymbol{\mathrm{a}}^{\mathrm{8}} +\boldsymbol{\mathrm{a}}^{\mathrm{4}} +\mathrm{1}}{\boldsymbol{\mathrm{a}}^{\mathrm{6}} +\mathrm{1}}. \\ $$$$\boldsymbol{\mathrm{solves}}.... \\ $$

Question Number 11476 Answers: 1 Comments: 0

Question Number 11423 Answers: 0 Comments: 0

please solve. ax^4 + bx^3 + cx^2 + dx + e = 0

$$\mathrm{please}\:\mathrm{solve}.\: \\ $$$$\mathrm{ax}^{\mathrm{4}} \:+\:\mathrm{bx}^{\mathrm{3}} \:+\:\mathrm{cx}^{\mathrm{2}} \:+\:\mathrm{dx}\:+\:\mathrm{e}\:=\:\mathrm{0} \\ $$

Question Number 11398 Answers: 0 Comments: 0

Solve for x : 625^(x − 5) = 200(√x^3 )

$$\mathrm{Solve}\:\mathrm{for}\:\mathrm{x}\:: \\ $$$$\mathrm{625}^{\mathrm{x}\:−\:\mathrm{5}} \:=\:\mathrm{200}\sqrt{\mathrm{x}^{\mathrm{3}} } \\ $$

Question Number 11363 Answers: 0 Comments: 0

x∈Z f(x)=log_3 (((x−5)/(x−2)))⇒Σx=?

$$\mathrm{x}\in\mathrm{Z} \\ $$$$\mathrm{f}\left(\mathrm{x}\right)=\mathrm{log}_{\mathrm{3}} \left(\frac{\mathrm{x}−\mathrm{5}}{\mathrm{x}−\mathrm{2}}\right)\Rightarrow\Sigma\mathrm{x}=? \\ $$

Question Number 11356 Answers: 1 Comments: 0

Question Number 11355 Answers: 1 Comments: 0

z+3−2i=(1+i)×z^− ⇒∣z∣=?

$$\mathrm{z}+\mathrm{3}−\mathrm{2i}=\left(\mathrm{1}+\mathrm{i}\right)×\overset{−} {\mathrm{z}}\:\Rightarrow\mid\mathrm{z}\mid=? \\ $$

Question Number 11334 Answers: 1 Comments: 0

z+∣z∣=9−3i⇒Re(z)

$$\mathrm{z}+\mid\mathrm{z}\mid=\mathrm{9}−\mathrm{3i}\Rightarrow\mathrm{Re}\left(\mathrm{z}\right) \\ $$

Question Number 11302 Answers: 2 Comments: 0

((sin10x−sin6x−sin2x)/(sin9x−sin7x−sinx))=?

$$\frac{\mathrm{sin10x}−\mathrm{sin6x}−\mathrm{sin2x}}{\mathrm{sin9x}−\mathrm{sin7x}−\mathrm{sinx}}=? \\ $$

Question Number 11285 Answers: 1 Comments: 0

((sin20)/(cos80−tan30×sin80))=?

$$\frac{{sin}\mathrm{20}}{{cos}\mathrm{80}−{tan}\mathrm{30}×{sin}\mathrm{80}}=? \\ $$

Question Number 11274 Answers: 2 Comments: 0

((sin20+(√3)×cos20)/(cos10))=?

$$\frac{{sin}\mathrm{20}+\sqrt{\mathrm{3}}×{cos}\mathrm{20}}{{cos}\mathrm{10}}=? \\ $$

Question Number 11268 Answers: 1 Comments: 0

Solve x, y and z in terms of p, q and r yz = py + qz ........ (i) zx = qz + rx ....... (ii) xy = rx + py ....... (iii)

$$\mathrm{Solve}\:\mathrm{x},\:\mathrm{y}\:\mathrm{and}\:\mathrm{z}\:\mathrm{in}\:\mathrm{terms}\:\mathrm{of}\:\mathrm{p},\:\mathrm{q}\:\mathrm{and}\:\mathrm{r} \\ $$$$\mathrm{yz}\:=\:\mathrm{py}\:+\:\mathrm{qz}\:\:\:\:\:........\:\left(\mathrm{i}\right) \\ $$$$\mathrm{zx}\:=\:\mathrm{qz}\:+\:\mathrm{rx}\:\:\:\:\:\:.......\:\left(\mathrm{ii}\right) \\ $$$$\mathrm{xy}\:=\:\mathrm{rx}\:+\:\mathrm{py}\:\:\:\:\:.......\:\left(\mathrm{iii}\right) \\ $$

Question Number 11263 Answers: 1 Comments: 0

Solve for x in the equation . 625^(x − 5) = 200(√x^3 )

$$\mathrm{Solve}\:\mathrm{for}\:\mathrm{x}\:\mathrm{in}\:\mathrm{the}\:\mathrm{equation}\:. \\ $$$$\mathrm{625}^{\mathrm{x}\:−\:\mathrm{5}} \:=\:\mathrm{200}\sqrt{\mathrm{x}^{\mathrm{3}} } \\ $$

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