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AlgebraQuestion and Answers: Page 231

Question Number 125258 Answers: 0 Comments: 1

a,b,c => ▲ tomonlari (p−a)(p−b)+(p−c)(p−a)+(p−b)(p−c)≥(√3) S

$${a},{b},{c}\:\:=>\:\:\blacktriangle\:\boldsymbol{{tomonlari}} \\ $$$$\left(\boldsymbol{{p}}−\boldsymbol{{a}}\right)\left(\boldsymbol{{p}}−\boldsymbol{{b}}\right)+\left(\boldsymbol{{p}}−\boldsymbol{{c}}\right)\left(\boldsymbol{{p}}−\boldsymbol{{a}}\right)+\left(\boldsymbol{{p}}−\boldsymbol{{b}}\right)\left(\boldsymbol{{p}}−\boldsymbol{{c}}\right)\geqslant\sqrt{\mathrm{3}}\:\boldsymbol{{S}} \\ $$

Question Number 125226 Answers: 0 Comments: 5

Question Number 125202 Answers: 2 Comments: 0

Solve the reccurence relation a_n = 2(a_(n−1) −a_(n−2) ) ; given a_0 =1 and a_1 = 0.

$$\:{Solve}\:{the}\:{reccurence}\:{relation} \\ $$$${a}_{{n}} \:=\:\mathrm{2}\left({a}_{{n}−\mathrm{1}} −{a}_{{n}−\mathrm{2}} \right)\:;\:{given}\:{a}_{\mathrm{0}} =\mathrm{1}\: \\ $$$${and}\:{a}_{\mathrm{1}} =\:\mathrm{0}. \\ $$

Question Number 125186 Answers: 1 Comments: 0

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algebra

$${algebra} \\ $$

Question Number 125136 Answers: 1 Comments: 3

Suppose a,b,c are nonzero real numbers satisfying (ab+bc+ca)^3 =abc(a+b+c)^3 . Provd that a,b,c must be terms of a Geometric Progession

$${Suppose}\:{a},{b},{c}\:{are}\:{nonzero}\:{real}\:{numbers} \\ $$$${satisfying}\:\left({ab}+{bc}+{ca}\right)^{\mathrm{3}} ={abc}\left({a}+{b}+{c}\right)^{\mathrm{3}} . \\ $$$${Provd}\:{that}\:{a},{b},{c}\:{must}\:{be}\:{terms}\:{of}\:{a}\:{Geometric} \\ $$$${Progession} \\ $$$$ \\ $$

Question Number 125132 Answers: 0 Comments: 0

Find the number of real roots of ax^7 −4x^4 +x^2 +1=0 where a>2

$${Find}\:{the}\:{number}\:{of}\:{real}\:{roots}\:{of}\:{ax}^{\mathrm{7}} −\mathrm{4}{x}^{\mathrm{4}} +{x}^{\mathrm{2}} +\mathrm{1}=\mathrm{0} \\ $$$${where}\:{a}>\mathrm{2} \\ $$

Question Number 125131 Answers: 0 Comments: 0

Let a,b,c∈ complex numbers such that the roots of the equation ax^2 +bx+c=0 have same modulus Prove that a=0 iff b=0

$${Let}\:{a},{b},{c}\in\:{complex}\:{numbers}\:{such}\:{that}\:{the}\:{roots} \\ $$$${of}\:{the}\:{equation}\:{ax}^{\mathrm{2}} +{bx}+{c}=\mathrm{0}\:{have}\:{same}\:{modulus} \\ $$$${Prove}\:{that}\:{a}=\mathrm{0}\:{iff}\:{b}=\mathrm{0} \\ $$

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Question Number 124963 Answers: 2 Comments: 1

∫_0 ^( (π/4)) ((sin(ς)dς)/(cos(ς)+sin(ς)))dς where ς : zeta

$$\int_{\mathrm{0}} ^{\:\frac{\pi}{\mathrm{4}}} \frac{\mathrm{sin}\left(\varsigma\right)\mathrm{d}\varsigma}{\mathrm{cos}\left(\varsigma\right)+\mathrm{sin}\left(\varsigma\right)}\mathrm{d}\varsigma \\ $$$$\mathrm{where}\:\varsigma\::\:\mathrm{zeta}\: \\ $$

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Question Number 125185 Answers: 1 Comments: 0

{ (((√x) + y = 11)),((x + (√y) = 7 )) :}

$$\:\begin{cases}{\sqrt{{x}}\:+\:{y}\:=\:\mathrm{11}}\\{{x}\:+\:\sqrt{{y}}\:=\:\mathrm{7}\:}\end{cases} \\ $$

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Question Number 124567 Answers: 1 Comments: 0

find the smallest integer which has 28 divisors and is divisible by 28.

$${find}\:{the}\:{smallest}\:{integer}\:{which}\:{has} \\ $$$$\mathrm{28}\:{divisors}\:{and}\:{is}\:{divisible}\:{by}\:\mathrm{28}. \\ $$

Question Number 124522 Answers: 1 Comments: 0

Question Number 124496 Answers: 0 Comments: 0

show that between 2 real numbers ∃ x,y s.t x<0 and y>0

$${show}\:{that}\:{between}\:\mathrm{2}\:{real}\:{numbers}\:\exists\:{x},{y}\:{s}.{t}\:{x}<\mathrm{0}\:{and}\:{y}>\mathrm{0} \\ $$

Question Number 124458 Answers: 0 Comments: 0

Question Number 124387 Answers: 1 Comments: 0

Solve x^2 −(1/2)x−7=x−3(√(2x^2 −3x+2)) for xεR .

$$\:{Solve}\:{x}^{\mathrm{2}} −\frac{\mathrm{1}}{\mathrm{2}}{x}−\mathrm{7}={x}−\mathrm{3}\sqrt{\mathrm{2}{x}^{\mathrm{2}} −\mathrm{3}{x}+\mathrm{2}} \\ $$$${for}\:{x}\epsilon{R}\:. \\ $$

Question Number 124375 Answers: 0 Comments: 0

Question Number 124314 Answers: 0 Comments: 1

{ ((x(√x) +y(√y) = 19)),((x(√y) +y(√x) = 15)) :}. find x+y { ((x(√x) +y(√y) = 133)),((y(√x) − x(√y) = 30)) :}. find x+y+xy { (((√x) +y = 53)),((x + (√y) = 23)) :}. find x+y

$$\begin{cases}{{x}\sqrt{{x}}\:+{y}\sqrt{{y}}\:=\:\mathrm{19}}\\{{x}\sqrt{{y}}\:+{y}\sqrt{{x}}\:=\:\mathrm{15}}\end{cases}.\:{find}\:{x}+{y} \\ $$$$\:\begin{cases}{{x}\sqrt{{x}}\:+{y}\sqrt{{y}}\:=\:\mathrm{133}}\\{{y}\sqrt{{x}}\:−\:{x}\sqrt{{y}}\:=\:\mathrm{30}}\end{cases}.\:{find}\:{x}+{y}+{xy} \\ $$$$\:\begin{cases}{\sqrt{{x}}\:+{y}\:=\:\mathrm{53}}\\{{x}\:+\:\sqrt{{y}}\:=\:\mathrm{23}}\end{cases}.\:{find}\:{x}+{y} \\ $$

Question Number 124312 Answers: 1 Comments: 0

3^x + 3^(−x) = 3 −(x−3)^2 x =?

$$\:\:\:\:\mathrm{3}^{{x}} \:+\:\mathrm{3}^{−{x}} \:=\:\mathrm{3}\:−\left({x}−\mathrm{3}\right)^{\mathrm{2}} \\ $$$$\:{x}\:=?\: \\ $$

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