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Question Number 201491 Answers: 6 Comments: 1

1. x^2 −1+((x^4 −x^2 ))^(1/3) =10x 2. (√(x−(1/x)))+(√(1−(1/x)))=x 3. (√(2x−(8/x)))+2(√(1−(2/x)))≥x 4. (√(x^2 +x))+(√(x+2))≥(√(3(x^2 −2x+2))) 5. ((√(x+5))−(√(x−3)))(1+(√(x^2 +2x−15)))≥8 6. x^2 +3x+1=(x+1)(√(x^2 +1)) 7. 2x^2 +3x+7=(x+5)(√(2x^2 +1))

$$\mathrm{1}.\:{x}^{\mathrm{2}} −\mathrm{1}+\sqrt[{\mathrm{3}}]{{x}^{\mathrm{4}} −{x}^{\mathrm{2}} }=\mathrm{10}{x} \\ $$$$\mathrm{2}.\:\sqrt{{x}−\frac{\mathrm{1}}{{x}}}+\sqrt{\mathrm{1}−\frac{\mathrm{1}}{{x}}}={x} \\ $$$$\mathrm{3}.\:\sqrt{\mathrm{2}{x}−\frac{\mathrm{8}}{{x}}}+\mathrm{2}\sqrt{\mathrm{1}−\frac{\mathrm{2}}{{x}}}\geqslant{x} \\ $$$$\mathrm{4}.\:\sqrt{{x}^{\mathrm{2}} +{x}}+\sqrt{{x}+\mathrm{2}}\geqslant\sqrt{\mathrm{3}\left({x}^{\mathrm{2}} −\mathrm{2}{x}+\mathrm{2}\right)} \\ $$$$\mathrm{5}.\:\left(\sqrt{{x}+\mathrm{5}}−\sqrt{{x}−\mathrm{3}}\right)\left(\mathrm{1}+\sqrt{{x}^{\mathrm{2}} +\mathrm{2}{x}−\mathrm{15}}\right)\geqslant\mathrm{8} \\ $$$$\mathrm{6}.\:{x}^{\mathrm{2}} +\mathrm{3}{x}+\mathrm{1}=\left({x}+\mathrm{1}\right)\sqrt{{x}^{\mathrm{2}} +\mathrm{1}} \\ $$$$\mathrm{7}.\:\mathrm{2}{x}^{\mathrm{2}} +\mathrm{3}{x}+\mathrm{7}=\left({x}+\mathrm{5}\right)\sqrt{\mathrm{2}{x}^{\mathrm{2}} +\mathrm{1}} \\ $$

Question Number 201308 Answers: 1 Comments: 2

Question Number 201302 Answers: 1 Comments: 0

{ ((x^2 + y^(−2) = 4)),((x^(−2) + y^2 = 5)) :} find: (y/x) = ?

$$\begin{cases}{\mathrm{x}^{\mathrm{2}} \:+\:\mathrm{y}^{−\mathrm{2}} \:=\:\mathrm{4}}\\{\mathrm{x}^{−\mathrm{2}} \:+\:\mathrm{y}^{\mathrm{2}} \:=\:\mathrm{5}}\end{cases}\:\:\:\:\:\mathrm{find}:\:\:\frac{\mathrm{y}}{\mathrm{x}}\:=\:? \\ $$

Question Number 201298 Answers: 1 Comments: 2

Question Number 201293 Answers: 1 Comments: 0

Question Number 201292 Answers: 1 Comments: 0

Question Number 201291 Answers: 2 Comments: 0

Question Number 201290 Answers: 1 Comments: 0

Question Number 201289 Answers: 3 Comments: 1

Question Number 201286 Answers: 0 Comments: 1

Question Number 201282 Answers: 1 Comments: 0

Question Number 201281 Answers: 0 Comments: 0

Question Number 201267 Answers: 0 Comments: 1

find ∫_0 ^1 (dx/((1+x)^(3/2) +(x−1)^(3/2) ))

$${find}\:\int_{\mathrm{0}} ^{\mathrm{1}} \frac{{dx}}{\left(\mathrm{1}+{x}\right)^{\frac{\mathrm{3}}{\mathrm{2}}} +\left({x}−\mathrm{1}\right)^{\frac{\mathrm{3}}{\mathrm{2}}} } \\ $$

Question Number 201266 Answers: 2 Comments: 0

calculate ∫_1 ^∞ (dx/( (√(1+x^3 ))))

$${calculate}\:\int_{\mathrm{1}} ^{\infty} \frac{{dx}}{\:\sqrt{\mathrm{1}+{x}^{\mathrm{3}} }} \\ $$

Question Number 201263 Answers: 2 Comments: 0

Q: the equation , sin^( 2) (x)−sin(mx)cos^2 (x)=1 has four distinct roots in ( 0 , 2π ) find the values of , m . (m ∈ N )

$$ \\ $$$$\:\:\:\:{Q}:\:{the}\:{equation}\:,\:{sin}^{\:\mathrm{2}} \left({x}\right)−{sin}\left({mx}\right){cos}\:^{\mathrm{2}} \left({x}\right)=\mathrm{1} \\ $$$$\:\:\:\:\:\:\:{has}\:\:{four}\:{distinct}\:{roots} \\ $$$$\:\:\:\:\:\:\:{in}\:\left(\:\mathrm{0}\:,\:\mathrm{2}\pi\:\right)\:\:{find}\:{the}\:{values} \\ $$$$\:\:\:\:\:\:\:\:{of}\:\:,\:\:\:{m}\:\:\:.\:\:\left({m}\:\in\:\mathbb{N}\:\right) \\ $$$$ \\ $$

Question Number 201258 Answers: 0 Comments: 0

Question Number 201257 Answers: 2 Comments: 0

Biggest prime factor of (3^(14) + 3^(13) − 12) = ?

$$\mathrm{Biggest}\:\mathrm{prime}\:\mathrm{factor}\:\mathrm{of}\:\left(\mathrm{3}^{\mathrm{14}} \:+\:\mathrm{3}^{\mathrm{13}} \:−\:\mathrm{12}\right)\:=\:? \\ $$

Question Number 201253 Answers: 2 Comments: 0

find the sum of n terms of the serice s_n =5+11+19+29+41+..........

$${find}\:{the}\:{sum}\:{of}\:{n}\:{terms}\:{of}\:{the}\:{serice} \\ $$$${s}_{{n}} =\mathrm{5}+\mathrm{11}+\mathrm{19}+\mathrm{29}+\mathrm{41}+.......... \\ $$

Question Number 201241 Answers: 0 Comments: 0

Question Number 201237 Answers: 1 Comments: 3

If , a ∣ 5b^( 2) −10b +1 ⇒ [ a , 5b ]_(lcm) = ?

$$ \\ $$$$\:\:\:\:{If}\:\:,\:\:\:{a}\:\mid\:\mathrm{5}{b}^{\:\mathrm{2}} −\mathrm{10}{b}\:+\mathrm{1}\: \\ $$$$\:\:\:\:\:\Rightarrow\:\:\:\left[\:{a}\:\:,\:\mathrm{5}{b}\:\right]_{\mathrm{lc}{m}} \:=\:\:?\: \\ $$$$ \\ $$$$ \\ $$

Question Number 201229 Answers: 1 Comments: 2

∫ (1/( (√(1+Inx))))dx

$$\int\:\frac{\mathrm{1}}{\:\sqrt{\mathrm{1}+\boldsymbol{{Inx}}}}\boldsymbol{{dx}} \\ $$

Question Number 201228 Answers: 0 Comments: 0

∫(√(x+(√(x+(√x))))) dx

$$\int\sqrt{\boldsymbol{{x}}+\sqrt{\boldsymbol{{x}}+\sqrt{\boldsymbol{{x}}}}}\:\boldsymbol{{dx}} \\ $$

Question Number 201227 Answers: 1 Comments: 0

∫ (((x^4 +x^7 )^(1/4) )/x^2 )dx

$$\:\int\:\frac{\left(\boldsymbol{{x}}^{\mathrm{4}} +\boldsymbol{{x}}^{\mathrm{7}} \right)^{\frac{\mathrm{1}}{\mathrm{4}}} }{\boldsymbol{{x}}^{\mathrm{2}} }\boldsymbol{{dx}} \\ $$

Question Number 201224 Answers: 2 Comments: 0

∫ (1/( (√(1+sinx))))dx

$$\int\:\frac{\mathrm{1}}{\:\sqrt{\mathrm{1}+\boldsymbol{{sinx}}}}\boldsymbol{{dx}} \\ $$

Question Number 201223 Answers: 1 Comments: 0

∫(√(1+(√(1+x)))) dx

$$\int\sqrt{\mathrm{1}+\sqrt{\mathrm{1}+\boldsymbol{{x}}}}\:\boldsymbol{{dx}} \\ $$

Question Number 201222 Answers: 1 Comments: 0

∫ (x^6 +x^9 )^(1/6) dx

$$\:\int\:\left(\boldsymbol{{x}}^{\mathrm{6}} +\boldsymbol{{x}}^{\mathrm{9}} \right)^{\frac{\mathrm{1}}{\mathrm{6}}} \boldsymbol{{dx}} \\ $$

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