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AlgebraQuestion and Answers: Page 357

Question Number 18299 Answers: 0 Comments: 2

x^x^x = 2, find x

$$\mathrm{x}^{\mathrm{x}^{\mathrm{x}} } \:=\:\mathrm{2},\:\:\:\:\:\:\mathrm{find}\:\:\mathrm{x} \\ $$

Question Number 18247 Answers: 0 Comments: 0

(((x+1)(x−1))/(x^2 +2x+3))

$$\frac{\left({x}+\mathrm{1}\right)\left({x}−\mathrm{1}\right)}{{x}^{\mathrm{2}} +\mathrm{2}{x}+\mathrm{3}} \\ $$

Question Number 18152 Answers: 0 Comments: 0

Question Number 18149 Answers: 1 Comments: 2

Question Number 18053 Answers: 0 Comments: 5

Question Number 17997 Answers: 0 Comments: 0

Solve on Z_(18) { (([6]_(18) x+[7]_(18) y=[1]_(18) )),(([2]_(18) x+[3]_(18) y=[11]_(18) )) :}

$${Solve}\:{on}\:\mathbb{Z}_{\mathrm{18}} \\ $$$$\begin{cases}{\left[\mathrm{6}\right]_{\mathrm{18}} {x}+\left[\mathrm{7}\right]_{\mathrm{18}} {y}=\left[\mathrm{1}\right]_{\mathrm{18}} }\\{\left[\mathrm{2}\right]_{\mathrm{18}} {x}+\left[\mathrm{3}\right]_{\mathrm{18}} {y}=\left[\mathrm{11}\right]_{\mathrm{18}} }\end{cases} \\ $$

Question Number 17985 Answers: 1 Comments: 0

solve simultaneously. x^3 + y^3 = 35 x^4 + y^4 = 97

$$\mathrm{solve}\:\mathrm{simultaneously}. \\ $$$$\mathrm{x}^{\mathrm{3}} \:+\:\mathrm{y}^{\mathrm{3}} \:=\:\mathrm{35} \\ $$$$\mathrm{x}^{\mathrm{4}} \:+\:\mathrm{y}^{\mathrm{4}} \:=\:\mathrm{97} \\ $$

Question Number 17775 Answers: 2 Comments: 0

Σ_(m=1) ^(10) (((sin 2πm)/(11)) − i((cos 2πm)/(11))) =????? Solve..it

$$\underset{{m}=\mathrm{1}} {\overset{\mathrm{10}} {\sum}}\left(\frac{\mathrm{sin}\:\mathrm{2}\pi{m}}{\mathrm{11}}\:−\:{i}\frac{\mathrm{cos}\:\mathrm{2}\pi{m}}{\mathrm{11}}\right)\:=????? \\ $$$${Solve}..{it} \\ $$$$ \\ $$

Question Number 17759 Answers: 1 Comments: 0

2^(4(y^2 −2)) =y^((y^2 −8)) please help me find y... pls!

$$\mathrm{2}^{\mathrm{4}\left(\mathrm{y}^{\mathrm{2}} −\mathrm{2}\right)} =\mathrm{y}^{\left(\mathrm{y}^{\mathrm{2}} −\mathrm{8}\right)} \\ $$$$ \\ $$$$ \\ $$$$\mathrm{please}\:\mathrm{help}\:\mathrm{me}\:\mathrm{find}\:\mathrm{y}...\:\mathrm{pls}! \\ $$

Question Number 17742 Answers: 1 Comments: 1

x^3 = 3^x , find x.

$$\mathrm{x}^{\mathrm{3}} \:=\:\mathrm{3}^{\mathrm{x}} ,\:\:\:\mathrm{find}\:\mathrm{x}. \\ $$

Question Number 17740 Answers: 0 Comments: 1

Question Number 17638 Answers: 0 Comments: 4

please help me with this confusing question x^(2x/y) ×y^(y/x) =4......(1) (xy)^(xy+yx) =16.....(2) solve for x and y

$$\mathrm{please}\:\mathrm{help}\:\mathrm{me}\:\mathrm{with}\:\mathrm{this} \\ $$$$\mathrm{confusing}\:\mathrm{question} \\ $$$$ \\ $$$$\mathrm{x}^{\mathrm{2x}/\mathrm{y}} ×\mathrm{y}^{\mathrm{y}/\mathrm{x}} =\mathrm{4}......\left(\mathrm{1}\right) \\ $$$$ \\ $$$$\left(\mathrm{xy}\right)^{\mathrm{xy}+\mathrm{yx}} =\mathrm{16}.....\left(\mathrm{2}\right) \\ $$$$ \\ $$$$\mathrm{solve}\:\mathrm{for}\:\mathrm{x}\:\mathrm{and}\:\mathrm{y} \\ $$

Question Number 17576 Answers: 1 Comments: 0

solve the equation x^y =y^x .......(1) x^2 =y^3 .......(2)

$$\mathrm{solve}\:\mathrm{the}\:\mathrm{equation} \\ $$$$ \\ $$$$\mathrm{x}^{\mathrm{y}} =\mathrm{y}^{\mathrm{x}} .......\left(\mathrm{1}\right) \\ $$$$ \\ $$$$\mathrm{x}^{\mathrm{2}} =\mathrm{y}^{\mathrm{3}} .......\left(\mathrm{2}\right) \\ $$

Question Number 17575 Answers: 0 Comments: 3

Question Number 17454 Answers: 1 Comments: 0

Find all integers n such that (n^2 − n − 1)^(n + 2) = 1

$$\mathrm{Find}\:\mathrm{all}\:\mathrm{integers}\:{n}\:\mathrm{such}\:\mathrm{that} \\ $$$$\left({n}^{\mathrm{2}} \:−\:{n}\:−\:\mathrm{1}\right)^{{n}\:+\:\mathrm{2}} \:=\:\mathrm{1} \\ $$

Question Number 17279 Answers: 0 Comments: 3

Is cosh^2 (3x) = (1/2)[1 + cos(6x)] ??????

$$\mathrm{Is}\:\:\mathrm{cosh}^{\mathrm{2}} \left(\mathrm{3x}\right)\:=\:\frac{\mathrm{1}}{\mathrm{2}}\left[\mathrm{1}\:+\:\mathrm{cos}\left(\mathrm{6x}\right)\right]\:\:?????? \\ $$

Question Number 17260 Answers: 1 Comments: 1

for a,b,c>0 prove that (ab+bc+ca)^2 ≥3(a+b+c)abc

$${for}\:{a},{b},{c}>\mathrm{0}\:{prove}\:{that} \\ $$$$\left({ab}+{bc}+{ca}\right)^{\mathrm{2}} \geqslant\mathrm{3}\left({a}+{b}+{c}\right){abc} \\ $$

Question Number 17065 Answers: 0 Comments: 4

if y=x^x what is the range of this function?

$$\mathrm{if}\:\mathrm{y}=\mathrm{x}^{\mathrm{x}} \\ $$$$\mathrm{what}\:\mathrm{is}\:\mathrm{the}\:\mathrm{range}\:\mathrm{of}\:\mathrm{this}\:\mathrm{function}? \\ $$

Question Number 17019 Answers: 1 Comments: 0

Σ_(r = 1) ^3 2r − 1 = ?

$$\underset{\mathrm{r}\:=\:\mathrm{1}} {\overset{\mathrm{3}} {\sum}}\:\mathrm{2r}\:−\:\mathrm{1}\:\:=\:\:? \\ $$

Question Number 17018 Answers: 0 Comments: 8

Find the cube root of: 55 + 63 (√2)

$$\mathrm{Find}\:\mathrm{the}\:\mathrm{cube}\:\mathrm{root}\:\mathrm{of}:\:\:\:\mathrm{55}\:+\:\mathrm{63}\:\sqrt{\mathrm{2}} \\ $$

Question Number 16990 Answers: 1 Comments: 4

If for positive integers a and b, a + b = (a/b) + (b/a), find a^2 + b^2 .

$$\mathrm{If}\:\mathrm{for}\:\mathrm{positive}\:\mathrm{integers}\:{a}\:\mathrm{and}\:{b}, \\ $$$${a}\:+\:{b}\:=\:\frac{{a}}{{b}}\:+\:\frac{{b}}{{a}},\:\mathrm{find}\:{a}^{\mathrm{2}} \:+\:{b}^{\mathrm{2}} . \\ $$

Question Number 16969 Answers: 0 Comments: 0

Question Number 16935 Answers: 1 Comments: 0

A two-digit number has the property that the square of its tens digit plus ten times its units digit is equal to the square of its units digit plus ten times its tens digit. Find all two digit numbers which have this property, and are prime numbers.

$$\mathrm{A}\:\mathrm{two}-\mathrm{digit}\:\mathrm{number}\:\mathrm{has}\:\mathrm{the}\:\mathrm{property} \\ $$$$\mathrm{that}\:\mathrm{the}\:\mathrm{square}\:\mathrm{of}\:\mathrm{its}\:\mathrm{tens}\:\mathrm{digit}\:\mathrm{plus} \\ $$$$\mathrm{ten}\:\mathrm{times}\:\mathrm{its}\:\mathrm{units}\:\mathrm{digit}\:\mathrm{is}\:\mathrm{equal}\:\mathrm{to}\:\mathrm{the} \\ $$$$\mathrm{square}\:\mathrm{of}\:\mathrm{its}\:\mathrm{units}\:\mathrm{digit}\:\mathrm{plus}\:\mathrm{ten}\:\mathrm{times} \\ $$$$\mathrm{its}\:\mathrm{tens}\:\mathrm{digit}.\:\mathrm{Find}\:\mathrm{all}\:\mathrm{two}\:\mathrm{digit} \\ $$$$\mathrm{numbers}\:\mathrm{which}\:\mathrm{have}\:\mathrm{this}\:\mathrm{property},\:\mathrm{and} \\ $$$$\mathrm{are}\:\mathrm{prime}\:\mathrm{numbers}. \\ $$

Question Number 16909 Answers: 1 Comments: 0

(√x^x^6 ) = 729 , Find x

$$\sqrt{\mathrm{x}^{\mathrm{x}^{\mathrm{6}} } }\:=\:\mathrm{729}\:,\:\:\:\:\mathrm{Find}\:\mathrm{x} \\ $$

Question Number 16906 Answers: 1 Comments: 0

x^x = 100, find x.

$$\mathrm{x}^{\mathrm{x}} \:=\:\mathrm{100},\:\mathrm{find}\:\mathrm{x}. \\ $$

Question Number 16881 Answers: 2 Comments: 0

The quadratic polynomials p(x) = a(x − 3)^2 + bx + 1 and q(x) = 2x^2 + c(x − 2) + 13 are equal for all values of x. Find the values of a, b, and c.

$$\mathrm{The}\:\mathrm{quadratic}\:\mathrm{polynomials} \\ $$$${p}\left({x}\right)\:=\:{a}\left({x}\:−\:\mathrm{3}\right)^{\mathrm{2}} \:+\:{bx}\:+\:\mathrm{1}\:\mathrm{and} \\ $$$${q}\left({x}\right)\:=\:\mathrm{2}{x}^{\mathrm{2}} \:+\:{c}\left({x}\:−\:\mathrm{2}\right)\:+\:\mathrm{13}\:\mathrm{are}\:\mathrm{equal} \\ $$$$\mathrm{for}\:\mathrm{all}\:\mathrm{values}\:\mathrm{of}\:{x}.\:\mathrm{Find}\:\mathrm{the}\:\mathrm{values}\:\mathrm{of}\:{a}, \\ $$$${b},\:\mathrm{and}\:{c}. \\ $$

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