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AlgebraQuestion and Answers: Page 289

Question Number 75267 Answers: 0 Comments: 5

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Question Number 75218 Answers: 1 Comments: 1

Simplify: (x^4 −3x^3 +4x^2 −12x) : (x^2 +4)

$$\mathrm{Simplify}:\:\left({x}^{\mathrm{4}} −\mathrm{3}{x}^{\mathrm{3}} +\mathrm{4}{x}^{\mathrm{2}} −\mathrm{12}{x}\right)\::\:\left({x}^{\mathrm{2}} +\mathrm{4}\right) \\ $$

Question Number 75176 Answers: 1 Comments: 0

P=(√(25x−50))−14(√((x−2)/4))+(√(9x−18)), x≥2 a) Simplify the equation b) Find x if P=3

$$\mathrm{P}=\sqrt{\mathrm{25}{x}−\mathrm{50}}−\mathrm{14}\sqrt{\frac{{x}−\mathrm{2}}{\mathrm{4}}}+\sqrt{\mathrm{9}{x}−\mathrm{18}},\:\:{x}\geqslant\mathrm{2} \\ $$$$\left.\mathrm{a}\right)\:\mathrm{Simplify}\:\mathrm{the}\:\mathrm{equation} \\ $$$$\left.\mathrm{b}\right)\:\mathrm{Find}\:\mathrm{x}\:\mathrm{if}\:\mathrm{P}=\mathrm{3} \\ $$

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{ ((x^2 =yz+1)),((y^2 =xz+2)),((z^2 =xy+3)) :} ⇒x+y+z=?

$$\begin{cases}{\boldsymbol{\mathrm{x}}^{\mathrm{2}} =\boldsymbol{\mathrm{yz}}+\mathrm{1}}\\{\boldsymbol{\mathrm{y}}^{\mathrm{2}} =\boldsymbol{\mathrm{xz}}+\mathrm{2}}\\{\boldsymbol{\mathrm{z}}^{\mathrm{2}} =\boldsymbol{\mathrm{xy}}+\mathrm{3}}\end{cases}\:\:\:\:\Rightarrow\boldsymbol{\mathrm{x}}+\boldsymbol{\mathrm{y}}+\boldsymbol{\mathrm{z}}=? \\ $$

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Explain a function with examples based on our daily life ?

$$\mathrm{Explain}\:\mathrm{a}\:\mathrm{function}\:\mathrm{with}\:\mathrm{examples}\:\mathrm{based} \\ $$$$\mathrm{on}\:\mathrm{our}\:\mathrm{daily}\:\mathrm{life}\:? \\ $$

Question Number 74880 Answers: 1 Comments: 0

solve inR ((∣x+1∣))^(1/5) −((x^2 +4x−9))^(1/(10)) =(2x−10)(√(x^2 +1))

$${solve}\:{inR} \\ $$$$\sqrt[{\mathrm{5}}]{\mid{x}+\mathrm{1}\mid}−\sqrt[{\mathrm{10}}]{{x}^{\mathrm{2}} +\mathrm{4}{x}−\mathrm{9}}=\left(\mathrm{2}{x}−\mathrm{10}\right)\sqrt{{x}^{\mathrm{2}} +\mathrm{1}} \\ $$

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{ ((x^2 +y^3 =23)),((x^3 +y^2 =32)) :} solve for x and y .

$$\begin{cases}{\boldsymbol{\mathrm{x}}^{\mathrm{2}} +\boldsymbol{\mathrm{y}}^{\mathrm{3}} =\mathrm{23}}\\{\boldsymbol{\mathrm{x}}^{\mathrm{3}} +\boldsymbol{\mathrm{y}}^{\mathrm{2}} =\mathrm{32}}\end{cases}\:\:\:\:\:\:\boldsymbol{\mathrm{solve}}\:\boldsymbol{\mathrm{for}}\:\boldsymbol{\mathrm{x}}\:\boldsymbol{\mathrm{and}}\:\boldsymbol{\mathrm{y}}\:. \\ $$

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If α and β are the roots of x^2 − x + 1 = 0, Find α^(23) + β^(23) without demoivre′s theorem.

$$\mathrm{If}\:\:\alpha\:\mathrm{and}\:\beta\:\mathrm{are}\:\mathrm{the}\:\mathrm{roots}\:\mathrm{of}\:\:\:\:\:\mathrm{x}^{\mathrm{2}} \:−\:\mathrm{x}\:+\:\mathrm{1}\:\:\:=\:\:\mathrm{0},\:\: \\ $$$$\mathrm{Find}\:\:\:\:\:\:\:\:\:\alpha^{\mathrm{23}} \:+\:\beta^{\mathrm{23}} \:\:\:\:\:\mathrm{without}\:\mathrm{demoivre}'\mathrm{s}\:\mathrm{theorem}. \\ $$

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Question Number 74663 Answers: 1 Comments: 0

If x^x y^y z^z = c show that at x = y = z (∂^2 z/(∂x∂y)) = − (x log ex)^(−1)

$$\mathrm{If}\:\:\:\:\mathrm{x}^{\mathrm{x}} \:\mathrm{y}^{\mathrm{y}} \:\mathrm{z}^{\mathrm{z}} \:\:\:=\:\:\:\mathrm{c}\:\:\:\:\:\:\:\mathrm{show}\:\mathrm{that}\:\mathrm{at}\:\:\:\:\:\mathrm{x}\:\:=\:\:\mathrm{y}\:\:=\:\:\mathrm{z} \\ $$$$\:\:\:\:\:\:\frac{\partial^{\mathrm{2}} \mathrm{z}}{\partial\mathrm{x}\partial\mathrm{y}}\:\:\:=\:\:\:−\:\left(\mathrm{x}\:\mathrm{log}\:\mathrm{ex}\right)^{−\mathrm{1}} \\ $$

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Hello,verry Nice day let U_n =E((((3+(√(17)))/2))^n ),n∈N^∗ show that U_n ≡n(2)

$$\mathrm{Hello},\mathrm{verry}\:\mathrm{Nice}\:\mathrm{day}\: \\ $$$$\mathrm{let}\:\mathrm{U}_{\mathrm{n}} =\mathrm{E}\left(\left(\frac{\mathrm{3}+\sqrt{\mathrm{17}}}{\mathrm{2}}\right)^{\mathrm{n}} \right),\mathrm{n}\in\mathbb{N}^{\ast} \\ $$$$\mathrm{show}\:\mathrm{that}\:\mathrm{U}_{\mathrm{n}} \equiv\mathrm{n}\left(\mathrm{2}\right) \\ $$

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Find the superimum of the set {(n^2 /2^n )}

$$\boldsymbol{{Find}}\:\boldsymbol{{the}}\:\boldsymbol{{superimum}}\:\boldsymbol{{of}}\:\boldsymbol{{the}}\:\boldsymbol{{set}}\:\left\{\frac{\boldsymbol{{n}}^{\mathrm{2}} }{\mathrm{2}^{\boldsymbol{{n}}} }\right\} \\ $$

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