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AlgebraQuestion and Answers: Page 70

Question Number 190073 Answers: 0 Comments: 0

Question Number 190039 Answers: 1 Comments: 0

b+(√b)−3=0 b>0 find 2b^2 −14b + 28 = ?

$$\mathrm{b}+\sqrt{\mathrm{b}}−\mathrm{3}=\mathrm{0} \\ $$$$\mathrm{b}>\mathrm{0} \\ $$$$\mathrm{find}\:\:\:\mathrm{2b}^{\mathrm{2}} −\mathrm{14b}\:+\:\mathrm{28}\:=\:? \\ $$

Question Number 190038 Answers: 1 Comments: 0

Find: ((21 + (√(4a − 3)))/(4a + (√(3 − 4a))))

$$\mathrm{Find}:\:\:\:\frac{\mathrm{21}\:+\:\sqrt{\mathrm{4a}\:−\:\mathrm{3}}}{\mathrm{4a}\:+\:\sqrt{\mathrm{3}\:−\:\mathrm{4a}}} \\ $$

Question Number 190035 Answers: 1 Comments: 0

10^(93) − 93 Find the sum of the numbers

$$\mathrm{10}^{\mathrm{93}} \:−\:\mathrm{93} \\ $$$$\mathrm{Find}\:\mathrm{the}\:\mathrm{sum}\:\mathrm{of}\:\mathrm{the}\:\mathrm{numbers} \\ $$

Question Number 190034 Answers: 3 Comments: 0

If x + (2/x) = (√(17)) Find: (((x^2 − 4)(x^2 − 1))/x^2 ) = ?

$$\mathrm{If}\:\:\:\mathrm{x}\:+\:\frac{\mathrm{2}}{\mathrm{x}}\:=\:\sqrt{\mathrm{17}} \\ $$$$\mathrm{Find}:\:\:\:\frac{\left(\mathrm{x}^{\mathrm{2}} \:−\:\mathrm{4}\right)\left(\mathrm{x}^{\mathrm{2}} \:−\:\mathrm{1}\right)}{\mathrm{x}^{\mathrm{2}} }\:=\:? \\ $$

Question Number 190032 Answers: 4 Comments: 0

x > 0 xy − 18 = 0 (2x + y)_(min) = ?

$$\mathrm{x}\:>\:\mathrm{0} \\ $$$$\mathrm{xy}\:−\:\mathrm{18}\:=\:\mathrm{0} \\ $$$$\left(\mathrm{2x}\:+\:\mathrm{y}\right)_{\boldsymbol{\mathrm{min}}} \:=\:? \\ $$

Question Number 190027 Answers: 1 Comments: 0

a^2 + b^2 = 12 ab = 4 Fund: a^3 + b^3 = ?

$$\mathrm{a}^{\mathrm{2}} \:+\:\mathrm{b}^{\mathrm{2}} \:=\:\mathrm{12} \\ $$$$\mathrm{ab}\:=\:\mathrm{4} \\ $$$$\mathrm{Fund}:\:\:\:\mathrm{a}^{\mathrm{3}} \:+\:\mathrm{b}^{\mathrm{3}} \:=\:? \\ $$

Question Number 190025 Answers: 1 Comments: 0

If f(x) = 3x^5 + 2x^2 Find: f((√2) − 1) + f(1 − (√2)) + 3

$$\mathrm{If}\:\:\:\mathrm{f}\left(\mathrm{x}\right)\:=\:\mathrm{3x}^{\mathrm{5}} \:+\:\mathrm{2x}^{\mathrm{2}} \\ $$$$\mathrm{Find}:\:\:\:\mathrm{f}\left(\sqrt{\mathrm{2}}\:−\:\mathrm{1}\right)\:+\:\mathrm{f}\left(\mathrm{1}\:−\:\sqrt{\mathrm{2}}\right)\:+\:\mathrm{3} \\ $$

Question Number 190024 Answers: 1 Comments: 0

Find: (√(4+(√2))) ∙ (√(3+(√(5+(√2))))) ∙ (√(3−(√(5+(√2))))) + ∣(√(14))−4∣

$$\mathrm{Find}: \\ $$$$\sqrt{\mathrm{4}+\sqrt{\mathrm{2}}}\:\centerdot\:\sqrt{\mathrm{3}+\sqrt{\mathrm{5}+\sqrt{\mathrm{2}}}}\:\centerdot\:\sqrt{\mathrm{3}−\sqrt{\mathrm{5}+\sqrt{\mathrm{2}}}}\:+\:\mid\sqrt{\mathrm{14}}−\mathrm{4}\mid \\ $$

Question Number 190022 Answers: 1 Comments: 2

5x^2 − 3x + 5 = 0 Find: x + (1/x) = 0

$$\mathrm{5x}^{\mathrm{2}} \:−\:\mathrm{3x}\:+\:\mathrm{5}\:=\:\mathrm{0} \\ $$$$\mathrm{Find}:\:\:\:\mathrm{x}\:+\:\frac{\mathrm{1}}{\mathrm{x}}\:=\:\mathrm{0} \\ $$

Question Number 189989 Answers: 1 Comments: 0

Question Number 189975 Answers: 1 Comments: 0

Question Number 190021 Answers: 0 Comments: 0

Find: lim_(n→∞) H_n (Σ_(k=1) ^n (1/(n+k)) -Σ_(k=1) ^n cot^(-1) (n+k))

$$\mathrm{Find}: \\ $$$$\underset{\boldsymbol{\mathrm{n}}\rightarrow\infty} {\mathrm{lim}}\:\mathrm{H}_{\boldsymbol{\mathrm{n}}} \:\left(\underset{\boldsymbol{\mathrm{k}}=\mathrm{1}} {\overset{\boldsymbol{\mathrm{n}}} {\sum}}\:\frac{\mathrm{1}}{\mathrm{n}+\mathrm{k}}\:-\underset{\boldsymbol{\mathrm{k}}=\mathrm{1}} {\overset{\boldsymbol{\mathrm{n}}} {\sum}}\:\mathrm{cot}^{-\mathrm{1}} \:\left(\mathrm{n}+\mathrm{k}\right)\right) \\ $$

Question Number 189952 Answers: 2 Comments: 0

(√2) sin(x) +cos(x)= −(√2)

$$\sqrt{\mathrm{2}}\:\mathrm{sin}\left(\mathrm{x}\right)\:+\mathrm{cos}\left(\mathrm{x}\right)=\:−\sqrt{\mathrm{2}}\: \\ $$

Question Number 189937 Answers: 0 Comments: 0

Question Number 189919 Answers: 1 Comments: 0

If x,y are real numbers satisfy ((x+40)/y)+((569)/(xy))=((26−y)/x) , then xy=?

$$\:{If}\:{x},{y}\:{are}\:{real}\:{numbers}\:{satisfy} \\ $$$$\:\frac{{x}+\mathrm{40}}{{y}}+\frac{\mathrm{569}}{{xy}}=\frac{\mathrm{26}−{y}}{{x}}\:,\:{then}\:{xy}=? \\ $$

Question Number 189916 Answers: 2 Comments: 0

when sinx×cosx=−(1/4) find sinx+cosx=?

$$\mathrm{when}\:\:\:\:\mathrm{sinx}×\mathrm{cosx}=−\frac{\mathrm{1}}{\mathrm{4}} \\ $$$$\mathrm{find}\:\:\:\:\:\:\:\mathrm{sinx}+\mathrm{cosx}=? \\ $$

Question Number 189886 Answers: 0 Comments: 0

e^( x) > 1+ x (∀ x >0 ) set: x=(√(π/e)) −1 e^( ((√π)/( (√e))) −1) > ((√π)/( (√e))) ⇒ e^( ((√π)/( (√e)))) > (√π) ( e^( ((√π)/( (√e)))) )^( (√e)) > (√π)^( (√e)) ⇒ e^( (√π)) > (√(π ))^( (√e))

$$ \\ $$$$\:\:{e}^{\:{x}} \:>\:\mathrm{1}+\:{x}\:\:\:\:\left(\forall\:{x}\:>\mathrm{0}\:\right) \\ $$$$\:\:\:{set}:\:{x}=\sqrt{\frac{\pi}{{e}}}\:−\mathrm{1} \\ $$$$\:\:\:\:{e}^{\:\frac{\sqrt{\pi}}{\:\sqrt{{e}}}\:−\mathrm{1}} >\:\frac{\sqrt{\pi}}{\:\sqrt{{e}}}\:\Rightarrow\:{e}^{\:\frac{\sqrt{\pi}}{\:\sqrt{{e}}}} \:>\:\sqrt{\pi}\: \\ $$$$\:\:\:\:\:\:\left(\:{e}^{\:\frac{\sqrt{\pi}}{\:\sqrt{{e}}}} \right)^{\:\sqrt{{e}}} >\:\sqrt{\pi}\:^{\:\sqrt{{e}}} \:\Rightarrow\:{e}^{\:\sqrt{\pi}} \:>\:\sqrt{\pi\:}\:^{\:\sqrt{{e}}} \\ $$$$ \\ $$

Question Number 189859 Answers: 0 Comments: 0

Question Number 189858 Answers: 1 Comments: 0

Question Number 189838 Answers: 0 Comments: 0

Question Number 189826 Answers: 0 Comments: 0

Question Number 189823 Answers: 0 Comments: 0

If: x_0 = 1 x_(n+1) = (√(x_n ^2 + x_n )) Find: Ω =lim_(n→∞) (x_n - (n/2) + (1/8) Σ_(k=1) ^(n−1) (1/x_k ))

$$\mathrm{If}:\:\:\:\mathrm{x}_{\mathrm{0}} \:=\:\mathrm{1} \\ $$$$\:\:\:\:\:\:\:\:\mathrm{x}_{\boldsymbol{\mathrm{n}}+\mathrm{1}} \:=\:\sqrt{\mathrm{x}_{\boldsymbol{\mathrm{n}}} ^{\mathrm{2}} \:+\:\mathrm{x}_{\boldsymbol{\mathrm{n}}} } \\ $$$$\mathrm{Find}:\:\:\:\Omega\:=\underset{\boldsymbol{\mathrm{n}}\rightarrow\infty} {\mathrm{lim}}\:\left(\mathrm{x}_{\boldsymbol{\mathrm{n}}} -\:\frac{\mathrm{n}}{\mathrm{2}}\:+\:\frac{\mathrm{1}}{\mathrm{8}}\:\underset{\boldsymbol{\mathrm{k}}=\mathrm{1}} {\overset{\boldsymbol{\mathrm{n}}−\mathrm{1}} {\sum}}\:\frac{\mathrm{1}}{\mathrm{x}_{\boldsymbol{\mathrm{k}}} }\right) \\ $$

Question Number 189803 Answers: 3 Comments: 0

what′s the minimum value of a+(1/(b(a−b))) where a>b>0 a,b∈R

$$ \\ $$$${what}'{s}\:{the}\:{minimum}\:{value}\:{of} \\ $$$${a}+\frac{\mathrm{1}}{{b}\left({a}−{b}\right)}\:{where}\:{a}>{b}>\mathrm{0}\:{a},{b}\in\mathbb{R} \\ $$$$ \\ $$

Question Number 189763 Answers: 0 Comments: 0

Question Number 189757 Answers: 2 Comments: 0

Find: lim_(x→(𝛑/2)) (((√2) ∣ sin 4x ∣)/( (√(1 − cos 4x)))) = ? Find: lim_(x→𝛑) (((√2) ∣ sin 6x ∣)/( (√(1 − cos 6x)))) = ?

$$\mathrm{Find}:\:\:\:\:\:\underset{\boldsymbol{\mathrm{x}}\rightarrow\frac{\boldsymbol{\pi}}{\mathrm{2}}} {\mathrm{lim}}\:\frac{\sqrt{\mathrm{2}}\:\mid\:\mathrm{sin}\:\mathrm{4x}\:\mid}{\:\sqrt{\mathrm{1}\:−\:\mathrm{cos}\:\mathrm{4x}}}\:\:\:=\:\:\:? \\ $$$$\mathrm{Find}:\:\:\:\:\:\underset{\boldsymbol{\mathrm{x}}\rightarrow\boldsymbol{\pi}} {\mathrm{lim}}\:\frac{\sqrt{\mathrm{2}}\:\mid\:\mathrm{sin}\:\mathrm{6x}\:\mid}{\:\sqrt{\mathrm{1}\:−\:\mathrm{cos}\:\mathrm{6x}}}\:\:\:=\:\:\:? \\ $$

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