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AlgebraQuestion and Answers: Page 222

Question Number 137097 Answers: 0 Comments: 0

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Question Number 136907 Answers: 4 Comments: 0

∫(√((2+x)/(2−x)))dx

$$\int\sqrt{\frac{\mathrm{2}+{x}}{\mathrm{2}−{x}}}{dx} \\ $$

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Given system equation { ((x^2 +3xy+y^2 +1=0)),((x^3 +y^3 −7=0)) :} has solution (x_1 ,y_1 ) &(x_2 ,y_2 ) for x,y∈R. Find the value of x_1 ^2 .y_2 +x_2 ^2 .y_1 .

$$\mathrm{Given}\:\mathrm{system}\:\mathrm{equation}\: \\ $$$$\:\begin{cases}{\mathrm{x}^{\mathrm{2}} +\mathrm{3xy}+\mathrm{y}^{\mathrm{2}} +\mathrm{1}=\mathrm{0}}\\{\mathrm{x}^{\mathrm{3}} +\mathrm{y}^{\mathrm{3}} −\mathrm{7}=\mathrm{0}}\end{cases}\:\mathrm{has}\:\mathrm{solution}\: \\ $$$$\left(\mathrm{x}_{\mathrm{1}} ,\mathrm{y}_{\mathrm{1}} \right)\:\&\left(\mathrm{x}_{\mathrm{2}} ,\mathrm{y}_{\mathrm{2}} \right)\:\mathrm{for}\:\mathrm{x},\mathrm{y}\in\mathbb{R}.\:\mathrm{Find}\:\mathrm{the}\:\mathrm{value} \\ $$$$\mathrm{of}\:\mathrm{x}_{\mathrm{1}} ^{\mathrm{2}} .\mathrm{y}_{\mathrm{2}} \:+\mathrm{x}_{\mathrm{2}} ^{\mathrm{2}} .\mathrm{y}_{\mathrm{1}} .\: \\ $$

Question Number 136741 Answers: 1 Comments: 0

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(√((√x)^(log x) ))=x faind x

$$\sqrt{\sqrt{{x}}\:^{\mathrm{log}\:{x}} }={x}\:\:\:\:\:\:\:{faind}\:\:{x} \\ $$

Question Number 136667 Answers: 2 Comments: 0

if f(x)=ax^2 +bx+c and f(5)=−3f(2) an intersiction point (−4,0) an the X-axis faind another point the X-axis

$${if}\:\:\:\:\:\:{f}\left({x}\right)={ax}^{\mathrm{2}} +{bx}+{c}\:\:\:\:\:\:{and}\:\:\:{f}\left(\mathrm{5}\right)=−\mathrm{3}{f}\left(\mathrm{2}\right) \\ $$$${an}\:{intersiction}\:\:{point}\:\:\left(−\mathrm{4},\mathrm{0}\right) \\ $$$${an}\:{the}\:\:{X}-{axis}\:\:\:\:\:{faind}\:{another}\:{point}\: \\ $$$${the}\:{X}-{axis} \\ $$$$ \\ $$

Question Number 136649 Answers: 0 Comments: 2

What the value of series (4/2) + (4.7/2.6) + (4.7.10/2.6.10) + (4.7.10.13/2.6.10.14) +…?

$$ \\ $$What the value of series (4/2) + (4.7/2.6) + (4.7.10/2.6.10) + (4.7.10.13/2.6.10.14) +…?

Question Number 136614 Answers: 1 Comments: 0

If a+(1/a) = 23 then (a)^(1/4) + (1/( (a)^(1/4) )) =?

$${If}\:{a}+\frac{\mathrm{1}}{{a}}\:=\:\mathrm{23}\:{then}\:\sqrt[{\mathrm{4}}]{{a}}\:+\:\frac{\mathrm{1}}{\:\sqrt[{\mathrm{4}}]{{a}}}\:=? \\ $$

Question Number 136607 Answers: 2 Comments: 0

What is the value of a^2 +b^2 if ax+by=3 bx−ay = 4 and x^2 +y^2 = 4

$$\mathrm{What}\:\mathrm{is}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\mathrm{a}^{\mathrm{2}} +\mathrm{b}^{\mathrm{2}} \:\mathrm{if}\:\mathrm{ax}+\mathrm{by}=\mathrm{3} \\ $$$$\mathrm{bx}−\mathrm{ay}\:=\:\mathrm{4}\:\mathrm{and}\:\mathrm{x}^{\mathrm{2}} +\mathrm{y}^{\mathrm{2}} \:=\:\mathrm{4} \\ $$

Question Number 136636 Answers: 0 Comments: 1

b=a+c y=x+c x=a+z y=b+z x=?,y=?,z=?

$${b}={a}+{c} \\ $$$${y}={x}+{c} \\ $$$${x}={a}+{z} \\ $$$${y}={b}+{z} \\ $$$${x}=?,{y}=?,{z}=? \\ $$

Question Number 136505 Answers: 1 Comments: 0

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5((√(1−x)) +(√(1+x)) )= 6x + 8(√(1−x^2 ))

$$\mathrm{5}\left(\sqrt{\mathrm{1}−{x}}\:+\sqrt{\mathrm{1}+{x}}\:\right)=\:\mathrm{6}{x}\:+\:\mathrm{8}\sqrt{\mathrm{1}−{x}^{\mathrm{2}} }\: \\ $$

Question Number 136489 Answers: 1 Comments: 0

(1/2)+(2/4)+(3/8)+(6/(16))+((11)/(32))+((20)/(64))+((37)/(128))+... =?

$$\frac{\mathrm{1}}{\mathrm{2}}+\frac{\mathrm{2}}{\mathrm{4}}+\frac{\mathrm{3}}{\mathrm{8}}+\frac{\mathrm{6}}{\mathrm{16}}+\frac{\mathrm{11}}{\mathrm{32}}+\frac{\mathrm{20}}{\mathrm{64}}+\frac{\mathrm{37}}{\mathrm{128}}+...\:=? \\ $$

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Question Number 136433 Answers: 1 Comments: 0

Σ_(k=0) ^n C_(2n+1) ^(2k+1) 8^k =...???

$$\underset{{k}=\mathrm{0}} {\overset{{n}} {\sum}}{C}_{\mathrm{2}{n}+\mathrm{1}} ^{\mathrm{2}{k}+\mathrm{1}} \mathrm{8}^{{k}} =...??? \\ $$

Question Number 136408 Answers: 2 Comments: 0

S=Σ_(k=0) ^∞ ((3k^2 )/(2k^3 +2)) =? =Σ_(k=0) ^∞ (1/2)(((3k^2 )/(k^3 +1)))=Σ_(k=0) ^∞ (1/2)[(1/(k+1))+((2k−1)/(k^2 −k+1))] I dont know how to continue...Please Help.

$$\:\:\:\:\:\:{S}=\underset{{k}=\mathrm{0}} {\overset{\infty} {\sum}}\:\:\frac{\mathrm{3}{k}^{\mathrm{2}} }{\mathrm{2}{k}^{\mathrm{3}} +\mathrm{2}}\:\:=? \\ $$$$\:\:\:\:\:\:\:\:\:=\underset{{k}=\mathrm{0}} {\overset{\infty} {\sum}}\frac{\mathrm{1}}{\mathrm{2}}\left(\frac{\mathrm{3}{k}^{\mathrm{2}} }{{k}^{\mathrm{3}} +\mathrm{1}}\right)=\underset{{k}=\mathrm{0}} {\overset{\infty} {\sum}}\frac{\mathrm{1}}{\mathrm{2}}\left[\frac{\mathrm{1}}{{k}+\mathrm{1}}+\frac{\mathrm{2}{k}−\mathrm{1}}{{k}^{\mathrm{2}} −{k}+\mathrm{1}}\right] \\ $$$$\:\:\:\:\:\:\:\:\:{I}\:{dont}\:{know}\:{how}\:{to}\:{continue}...{Please}\:{Help}. \\ $$$$ \\ $$

Question Number 136340 Answers: 1 Comments: 0

If (√(3+(√2))) = (√((a+(√b))/c)) + (√((a−(√b))/c)) then a+bc = ?

$${If}\:\sqrt{\mathrm{3}+\sqrt{\mathrm{2}}}\:=\:\sqrt{\frac{{a}+\sqrt{{b}}}{{c}}}\:+\:\sqrt{\frac{{a}−\sqrt{{b}}}{{c}}} \\ $$$${then}\:{a}+{bc}\:=\:? \\ $$

Question Number 136283 Answers: 1 Comments: 0

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