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AlgebraQuestion and Answers: Page 46

Question Number 204461 Answers: 2 Comments: 0

Solve for x (x − 12)(x − 13) = ((34)/(33^2 ))

$$\mathrm{Solve}\:\mathrm{for}\:{x} \\ $$$$\left({x}\:−\:\mathrm{12}\right)\left({x}\:−\:\mathrm{13}\right)\:=\:\frac{\mathrm{34}}{\mathrm{33}^{\mathrm{2}} } \\ $$

Question Number 204421 Answers: 3 Comments: 0

x^3 +y^3 = 35 (1/x)+(1/y) =(5/6) solve for all possible values of x and y

$${x}^{\mathrm{3}} +{y}^{\mathrm{3}} \:=\:\mathrm{35} \\ $$$$\frac{\mathrm{1}}{{x}}+\frac{\mathrm{1}}{{y}}\:=\frac{\mathrm{5}}{\mathrm{6}} \\ $$$${solve}\:{for}\:{all}\:{possible}\:{values}\:{of}\:{x}\:{and}\:{y} \\ $$$$ \\ $$

Question Number 204417 Answers: 2 Comments: 0

Solve for z∈C e^z =ln z

$$\mathrm{Solve}\:\mathrm{for}\:{z}\in\mathbb{C} \\ $$$$ \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{e}^{{z}} =\mathrm{ln}\:{z} \\ $$

Question Number 204410 Answers: 0 Comments: 0

Question Number 204398 Answers: 0 Comments: 0

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Question Number 204397 Answers: 3 Comments: 0

Question Number 204384 Answers: 0 Comments: 1

Question Number 204350 Answers: 1 Comments: 0

Question Number 204349 Answers: 1 Comments: 2

Question Number 204334 Answers: 2 Comments: 0

Question Number 204330 Answers: 1 Comments: 0

Question Number 204329 Answers: 2 Comments: 0

solve (1/([x]))+(1/([2x]))={x}+(1/3)

$${solve}\:\frac{\mathrm{1}}{\left[{x}\right]}+\frac{\mathrm{1}}{\left[\mathrm{2}{x}\right]}=\left\{{x}\right\}+\frac{\mathrm{1}}{\mathrm{3}} \\ $$

Question Number 204249 Answers: 2 Comments: 1

Question Number 204270 Answers: 2 Comments: 0

Question Number 204218 Answers: 2 Comments: 0

Question Number 204211 Answers: 2 Comments: 0

Question Number 204205 Answers: 4 Comments: 0

Question Number 204187 Answers: 2 Comments: 0

If p , q , r >0 , pqr= 1 ⇒ min((( p^3 )/(q+r)) + (q^( 3) /(p+r)) +(r^3 /(p+q)) )=? ∗ give a reason ∗

$$ \\ $$$$\:\:\:\:\:\:{If}\:\:\:{p}\:,\:{q}\:,\:{r}\:>\mathrm{0}\:,\:\:{pqr}=\:\mathrm{1} \\ $$$$\:\:\:\:\: \\ $$$$\:\Rightarrow\:\:{min}\left(\frac{\:{p}^{\mathrm{3}} }{{q}+{r}}\:+\:\frac{{q}^{\:\mathrm{3}} }{{p}+{r}}\:+\frac{{r}^{\mathrm{3}} }{{p}+{q}}\:\right)=? \\ $$$$\:\:\:\ast\:{give}\:{a}\:{reason}\:\ast \\ $$

Question Number 204179 Answers: 2 Comments: 0

Question Number 204158 Answers: 2 Comments: 2

Question Number 204152 Answers: 2 Comments: 0

the maximum value of f(x,y) = xy−x^3 y^2 attained over the square 0≤x≤1;0≤y≤1 is

$$\:\:\mathrm{the}\:\mathrm{maximum}\:\mathrm{value}\:\mathrm{of}\:\mathrm{f}\left(\mathrm{x},\mathrm{y}\right)\:=\:\mathrm{xy}−\mathrm{x}^{\mathrm{3}} \mathrm{y}^{\mathrm{2}} \\ $$$$\:\mathrm{attained}\:\mathrm{over}\:\mathrm{the}\:\mathrm{square}\:\mathrm{0}\leqslant\mathrm{x}\leqslant\mathrm{1};\mathrm{0}\leqslant\mathrm{y}\leqslant\mathrm{1}\:\mathrm{is} \\ $$

Question Number 204129 Answers: 2 Comments: 0

a , b , x , y ∈ R a + b = 23 ax + by = 79 ax^2 + by^2 = 217 ax^3 + by^3 = 661 Find: ax^4 + by^4 = ?

$$\mathrm{a}\:,\:\mathrm{b}\:,\:\mathrm{x}\:,\:\mathrm{y}\:\in\:\mathbb{R} \\ $$$$\mathrm{a}\:+\:\mathrm{b}\:=\:\mathrm{23} \\ $$$$\mathrm{ax}\:+\:\mathrm{by}\:=\:\mathrm{79} \\ $$$$\mathrm{ax}^{\mathrm{2}} \:+\:\mathrm{by}^{\mathrm{2}} \:=\:\mathrm{217} \\ $$$$\mathrm{ax}^{\mathrm{3}} \:+\:\mathrm{by}^{\mathrm{3}} \:=\:\mathrm{661} \\ $$$$\mathrm{Find}:\:\:\:\mathrm{ax}^{\mathrm{4}} \:+\:\mathrm{by}^{\mathrm{4}} \:=\:? \\ $$

Question Number 204123 Answers: 2 Comments: 1

Question Number 204082 Answers: 1 Comments: 3

(√(((√(x^2 +66^2 ))+x)/x))−(√(x(√(x^2 +66^2 ))−x^2 ))=5

$$\sqrt{\frac{\sqrt{{x}^{\mathrm{2}} +\mathrm{66}^{\mathrm{2}} }+{x}}{{x}}}−\sqrt{{x}\sqrt{{x}^{\mathrm{2}} +\mathrm{66}^{\mathrm{2}} }−{x}^{\mathrm{2}} }=\mathrm{5} \\ $$

Question Number 204056 Answers: 2 Comments: 0

{ ((x + 2y + z = 8)),((3x + 2y + z = 10)),((4x + 3y − 2z = 4)) :} Solve with the help of matrix

$$\begin{cases}{\mathrm{x}\:+\:\mathrm{2y}\:+\:\mathrm{z}\:=\:\mathrm{8}}\\{\mathrm{3x}\:+\:\mathrm{2y}\:+\:\mathrm{z}\:=\:\mathrm{10}}\\{\mathrm{4x}\:+\:\mathrm{3y}\:−\:\mathrm{2z}\:=\:\mathrm{4}}\end{cases} \\ $$$$\mathrm{Solve}\:\mathrm{with}\:\mathrm{the}\:\mathrm{help}\:\mathrm{of}\:\mathrm{matrix} \\ $$

Question Number 204055 Answers: 2 Comments: 0

y = (2/3) arctg (x^4 ) find: y^′ = ?

$$\mathrm{y}\:=\:\frac{\mathrm{2}}{\mathrm{3}}\:\mathrm{arctg}\:\left(\mathrm{x}^{\mathrm{4}} \right) \\ $$$$\mathrm{find}:\:\:\mathrm{y}^{'} \:=\:? \\ $$

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