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Question Number 55195 Answers: 1 Comments: 0

x^2 +ax+(√2)b=0,has 2 roots:c and d,also x^2 +cx+(√2)d=0,has 2 roots:a and b.such that:a, b, c, d,are defferent non zero numbers. find possible value(s) for:a^2 +b^2 +c^2 +d^2 .

$$\boldsymbol{\mathrm{x}}^{\mathrm{2}} +\boldsymbol{\mathrm{ax}}+\sqrt{\mathrm{2}}\boldsymbol{\mathrm{b}}=\mathrm{0},\boldsymbol{\mathrm{has}}\:\mathrm{2}\:\boldsymbol{\mathrm{roots}}:\boldsymbol{\mathrm{c}}\:\boldsymbol{\mathrm{and}}\:\boldsymbol{\mathrm{d}},\boldsymbol{\mathrm{also}} \\ $$$$\boldsymbol{\mathrm{x}}^{\mathrm{2}} +\boldsymbol{\mathrm{cx}}+\sqrt{\mathrm{2}}\boldsymbol{\mathrm{d}}=\mathrm{0},\boldsymbol{\mathrm{has}}\:\mathrm{2}\:\boldsymbol{\mathrm{roots}}:\boldsymbol{\mathrm{a}}\:\boldsymbol{\mathrm{and}}\:\boldsymbol{\mathrm{b}}.\boldsymbol{\mathrm{such}} \\ $$$$\boldsymbol{\mathrm{that}}:\boldsymbol{\mathrm{a}},\:\boldsymbol{\mathrm{b}},\:\boldsymbol{\mathrm{c}},\:\boldsymbol{\mathrm{d}},\boldsymbol{\mathrm{are}}\:\boldsymbol{\mathrm{defferent}}\:\boldsymbol{\mathrm{non}}\:\boldsymbol{\mathrm{zero}}\: \\ $$$$\boldsymbol{\mathrm{numbers}}. \\ $$$$\boldsymbol{\mathrm{find}}\:\boldsymbol{\mathrm{possible}}\:\boldsymbol{\mathrm{value}}\left(\boldsymbol{\mathrm{s}}\right)\:\boldsymbol{\mathrm{for}}:\boldsymbol{\mathrm{a}}^{\mathrm{2}} +\boldsymbol{\mathrm{b}}^{\mathrm{2}} +\boldsymbol{\mathrm{c}}^{\mathrm{2}} +\boldsymbol{\mathrm{d}}^{\mathrm{2}} . \\ $$

Question Number 55193 Answers: 1 Comments: 0

Question Number 55192 Answers: 1 Comments: 1

what will be the numbers of zeroes in the expension of a) 100!×25! b) 100!+25! please help

$${what}\:{will}\:{be}\:{the}\:{numbers}\:{of}\:{zeroes}\:{in}\:{the}\:{expension}\:{of} \\ $$$$\left.{a}\right)\:\mathrm{100}!×\mathrm{25}! \\ $$$$\left.{b}\right)\:\mathrm{100}!+\mathrm{25}! \\ $$$$ \\ $$$${please}\:{help} \\ $$

Question Number 55191 Answers: 2 Comments: 0

Question Number 55185 Answers: 0 Comments: 3

Question Number 55174 Answers: 0 Comments: 3

center and radius convergence of series Σ_(n=0) ^(∝) (((4−2i)/(1+5i)))^n z^n is...

$$\mathrm{center}\:\mathrm{and}\:\mathrm{radius}\:\mathrm{convergence} \\ $$$$\:\mathrm{of}\:\mathrm{series}\:\underset{{n}=\mathrm{0}} {\overset{\propto} {\Sigma}}\:\left(\frac{\mathrm{4}−\mathrm{2}{i}}{\mathrm{1}+\mathrm{5}{i}}\right)^{{n}} {z}^{{n}} \:\mathrm{is}... \\ $$$$ \\ $$

Question Number 55172 Answers: 1 Comments: 0

Question Number 55171 Answers: 0 Comments: 3

Question Number 55166 Answers: 1 Comments: 0

Question Number 55190 Answers: 1 Comments: 0

Question Number 55150 Answers: 2 Comments: 0

Question Number 55149 Answers: 1 Comments: 0

Question Number 55141 Answers: 2 Comments: 1

prove the following identities a.((sin θ)/(1+cos 2θ))=tan θ b.((1−cos 2θ−sin θ)/(sin 2θ−cos θ))=tan θ c.((cos (x+y)+sin (x−y))/(cos 2ycos 2x))=(1/(cos (x+y)sin (y−x)))

$${prove}\:{the}\:{following}\:{identities} \\ $$$$ \\ $$$${a}.\frac{\mathrm{sin}\:\theta}{\mathrm{1}+\mathrm{cos}\:\mathrm{2}\theta}=\mathrm{tan}\:\theta \\ $$$${b}.\frac{\mathrm{1}−\mathrm{cos}\:\mathrm{2}\theta−\mathrm{sin}\:\theta}{\mathrm{sin}\:\mathrm{2}\theta−\mathrm{cos}\:\theta}=\mathrm{tan}\:\theta \\ $$$${c}.\frac{\mathrm{cos}\:\left({x}+{y}\right)+\mathrm{sin}\:\left({x}−{y}\right)}{\mathrm{cos}\:\mathrm{2}{y}\mathrm{cos}\:\mathrm{2}{x}}=\frac{\mathrm{1}}{\mathrm{cos}\:\left({x}+{y}\right)\mathrm{sin}\:\left({y}−{x}\right)} \\ $$

Question Number 55138 Answers: 0 Comments: 1

Question Number 55129 Answers: 1 Comments: 1

question 54995 reposted ∫((x^3 +x^2 ))^(1/3) dx=?

$$\mathrm{question}\:\mathrm{54995}\:\mathrm{reposted} \\ $$$$\int\sqrt[{\mathrm{3}}]{{x}^{\mathrm{3}} +{x}^{\mathrm{2}} }{dx}=? \\ $$

Question Number 55126 Answers: 0 Comments: 0

Question Number 55119 Answers: 1 Comments: 1

How many numbers, divisible by 5, can be made with the digits 2,3,4 and 5 where no digit is being used more than once in each number?

$$\mathrm{How}\:\mathrm{many}\:\mathrm{numbers},\:\mathrm{divisible}\:\mathrm{by}\:\mathrm{5},\:\mathrm{can} \\ $$$$\mathrm{be}\:\mathrm{made}\:\mathrm{with}\:\mathrm{the}\:\mathrm{digits}\:\mathrm{2},\mathrm{3},\mathrm{4}\:\mathrm{and}\:\mathrm{5}\:\mathrm{where} \\ $$$$\mathrm{no}\:\mathrm{digit}\:\mathrm{is}\:\mathrm{being}\:\mathrm{used}\:\mathrm{more}\:\mathrm{than}\:\mathrm{once} \\ $$$$\mathrm{in}\:\mathrm{each}\:\mathrm{number}? \\ $$

Question Number 55115 Answers: 0 Comments: 4

Question Number 55108 Answers: 0 Comments: 0

Question Number 55104 Answers: 0 Comments: 3

Question Number 55100 Answers: 1 Comments: 5

Question Number 55099 Answers: 1 Comments: 0

Show that for n ∈ N, Σ_(r=0) ^n P_r ^n = ⌊n! e⌋ where ⌊x⌋ denotes the greatest integer ≤ x and P_r ^n = ((n!)/((n − r)!))

$$\mathrm{Show}\:\mathrm{that}\:\mathrm{for}\:{n}\:\in\:\mathbb{N}, \\ $$$$\underset{{r}=\mathrm{0}} {\overset{{n}} {\sum}}\:{P}_{{r}} ^{{n}} \:=\:\lfloor{n}!\:{e}\rfloor \\ $$$$\mathrm{where}\:\lfloor{x}\rfloor\:\mathrm{denotes}\:\mathrm{the}\:\mathrm{greatest}\:\mathrm{integer}\:\leqslant\:{x} \\ $$$$\mathrm{and}\:{P}_{{r}} ^{{n}} \:=\:\frac{{n}!}{\left({n}\:−\:{r}\right)!} \\ $$

Question Number 55089 Answers: 0 Comments: 1

∫_( 0) ^1 (1/((x^2 +1)^(3/2) )) dx =

$$\:\underset{\:\mathrm{0}} {\overset{\mathrm{1}} {\int}}\:\:\frac{\mathrm{1}}{\left({x}^{\mathrm{2}} +\mathrm{1}\right)^{\mathrm{3}/\mathrm{2}} }\:{dx}\:= \\ $$

Question Number 55088 Answers: 0 Comments: 0

Question Number 55087 Answers: 0 Comments: 1

Please any web site or ebook to learn LATEX ? Thank you.

$$\mathrm{Please}\:\mathrm{any}\:\mathrm{web}\:\mathrm{site}\:\mathrm{or}\:\mathrm{ebook}\:\mathrm{to}\:\mathrm{learn} \\ $$$${LATEX}\:? \\ $$$$\mathrm{Thank}\:\mathrm{you}. \\ $$

Question Number 55094 Answers: 2 Comments: 2

(((1/4) + (1/(16)) + (1/(36)) + (1/(64)) + ...)/(1 + (1/9) + (1/(25)) + (1/(49)) + ...)) = x 3x^2 + 2x − 1 = ?

$$\frac{\frac{\mathrm{1}}{\mathrm{4}}\:+\:\frac{\mathrm{1}}{\mathrm{16}}\:+\:\frac{\mathrm{1}}{\mathrm{36}}\:+\:\frac{\mathrm{1}}{\mathrm{64}}\:+\:...}{\mathrm{1}\:+\:\frac{\mathrm{1}}{\mathrm{9}}\:+\:\frac{\mathrm{1}}{\mathrm{25}}\:+\:\frac{\mathrm{1}}{\mathrm{49}}\:+\:...}\:\:=\:\:{x} \\ $$$$\mathrm{3}{x}^{\mathrm{2}} \:+\:\mathrm{2}{x}\:−\:\mathrm{1}\:\:=\:\:? \\ $$

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