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AlgebraQuestion and Answers: Page 253

Question Number 90086 Answers: 0 Comments: 7

Question Number 90092 Answers: 0 Comments: 1

G((√(x+5))) = x G(x^2 ) = x^a −b find a+b

$$\mathrm{G}\left(\sqrt{\mathrm{x}+\mathrm{5}}\right)\:=\:\mathrm{x} \\ $$$$\mathrm{G}\left(\mathrm{x}^{\mathrm{2}} \right)\:=\:\mathrm{x}^{\mathrm{a}} −\mathrm{b} \\ $$$$\mathrm{find}\:\mathrm{a}+\mathrm{b}\: \\ $$

Question Number 90048 Answers: 1 Comments: 0

5^(√x) −5^(x−7) = 100

$$\mathrm{5}^{\sqrt{\mathrm{x}}} \:−\mathrm{5}^{\mathrm{x}−\mathrm{7}} \:=\:\mathrm{100} \\ $$

Question Number 90038 Answers: 0 Comments: 0

Σ_(n=1) ^∞ (H_n /n^k )=S_k H_q =Σ_(p=1) ^q (1/p) Is there a simple from for S_k

$$\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{{H}_{{n}} }{{n}^{{k}} }={S}_{{k}} \:\:\:\:\:\:\:{H}_{{q}} =\underset{{p}=\mathrm{1}} {\overset{{q}} {\sum}}\frac{\mathrm{1}}{{p}} \\ $$$${Is}\:{there}\:{a}\:{simple}\:{from}\:{for}\:{S}_{{k}} \\ $$

Question Number 90030 Answers: 0 Comments: 0

Question Number 89991 Answers: 0 Comments: 2

if a,b > 0 and (a^2 /b^2 ) = (5/3) find ((a^2 +b^2 )/(ab))

$$\mathrm{if}\:\mathrm{a},\mathrm{b}\:>\:\mathrm{0}\:\mathrm{and}\:\frac{\mathrm{a}^{\mathrm{2}} }{\mathrm{b}^{\mathrm{2}} }\:=\:\frac{\mathrm{5}}{\mathrm{3}} \\ $$$$\mathrm{find}\:\frac{\mathrm{a}^{\mathrm{2}} +\mathrm{b}^{\mathrm{2}} }{\mathrm{ab}} \\ $$

Question Number 89977 Answers: 0 Comments: 2

Question Number 89955 Answers: 1 Comments: 2

9^(x+1) ∤28(3^x )+3=0

$$\mathrm{9}^{\mathrm{x}+\mathrm{1}} \nmid\mathrm{28}\left(\mathrm{3}^{\mathrm{x}} \right)+\mathrm{3}=\mathrm{0} \\ $$

Question Number 89938 Answers: 0 Comments: 1

If x(x+1) = 1 find (x+1)^3 −(1/((x+1)^3 ))

$$\mathrm{If}\:\mathrm{x}\left(\mathrm{x}+\mathrm{1}\right)\:=\:\mathrm{1}\: \\ $$$$\mathrm{find}\:\left(\mathrm{x}+\mathrm{1}\right)^{\mathrm{3}} −\frac{\mathrm{1}}{\left(\mathrm{x}+\mathrm{1}\right)^{\mathrm{3}} } \\ $$

Question Number 89928 Answers: 1 Comments: 0

Question Number 89907 Answers: 1 Comments: 0

If the sum of 4 numbers is between 53 and 57 then the arithmetic mean of the numbers could be one of the following a)11.5 b)12 c)12.5 d)13 e)14

$${If}\:{the}\:{sum}\:{of}\:\mathrm{4}\:{numbers}\:{is}\:{between} \\ $$$$\mathrm{53}\:{and}\:\mathrm{57}\:{then}\:{the}\:{arithmetic}\:{mean}\:{of} \\ $$$${the}\:{numbers}\:{could}\:{be}\:{one}\:{of}\:{the} \\ $$$${following} \\ $$$$ \\ $$$$\left.{a}\left.\right)\left.\mathrm{1}\left.\mathrm{1}\left..\mathrm{5}\:{b}\right)\mathrm{12}\:{c}\right)\mathrm{12}.\mathrm{5}\:{d}\right)\mathrm{13}\:{e}\right)\mathrm{14} \\ $$

Question Number 89834 Answers: 1 Comments: 1

Find x e^x = x^2 −1 anyother method apart from Newton′s

$${Find}\:{x}\: \\ $$$$\boldsymbol{{e}}^{\boldsymbol{{x}}} =\:\boldsymbol{{x}}^{\mathrm{2}} −\mathrm{1} \\ $$$$\boldsymbol{{anyother}}\:\boldsymbol{{method}}\:\boldsymbol{{apart}}\:\boldsymbol{{from}}\:\boldsymbol{{N}}{ewton}'{s} \\ $$

Question Number 89829 Answers: 0 Comments: 9

Question Number 89826 Answers: 0 Comments: 0

Solve the equation: x^2 + xy + y^2 = 7 ...... (i) y^2 + yz + z^2 = 3 ...... (ii) z^2 + xz + x^2 = 1 ..... (iii)

$$\mathrm{Solve}\:\mathrm{the}\:\mathrm{equation}: \\ $$$$\:\:\:\:\:\:\mathrm{x}^{\mathrm{2}} \:\:+\:\:\mathrm{xy}\:\:+\:\:\mathrm{y}^{\mathrm{2}} \:\:\:=\:\:\:\mathrm{7}\:\:\:\:\:\:\:\:\:......\:\left(\mathrm{i}\right) \\ $$$$\:\:\:\:\:\:\mathrm{y}^{\mathrm{2}} \:\:+\:\:\mathrm{yz}\:\:+\:\:\mathrm{z}^{\mathrm{2}} \:\:\:=\:\:\:\mathrm{3}\:\:\:\:\:\:\:\:\:\:......\:\left(\mathrm{ii}\right) \\ $$$$\:\:\:\:\:\:\mathrm{z}^{\mathrm{2}} \:\:+\:\:\mathrm{xz}\:\:+\:\:\mathrm{x}^{\mathrm{2}} \:\:\:=\:\:\:\mathrm{1}\:\:\:\:\:\:\:\:\:\:.....\:\left(\mathrm{iii}\right) \\ $$

Question Number 89795 Answers: 1 Comments: 0

Question Number 89794 Answers: 0 Comments: 1

true or false (1+(1/1^3 ))(1+(1/2^3 ))(1+(1/3^3 )).....(1+(1/n^3 ))<3

$${true}\:{or}\:{false} \\ $$$$\left(\mathrm{1}+\frac{\mathrm{1}}{\mathrm{1}^{\mathrm{3}} }\right)\left(\mathrm{1}+\frac{\mathrm{1}}{\mathrm{2}^{\mathrm{3}} }\right)\left(\mathrm{1}+\frac{\mathrm{1}}{\mathrm{3}^{\mathrm{3}} }\right).....\left(\mathrm{1}+\frac{\mathrm{1}}{{n}^{\mathrm{3}} }\right)<\mathrm{3} \\ $$

Question Number 89920 Answers: 0 Comments: 1

x=(1/(1+(1/(1+x)))) and y=(2/(2+(1/(1+y )))) find x+y

$${x}=\frac{\mathrm{1}}{\mathrm{1}+\frac{\mathrm{1}}{\mathrm{1}+{x}}}\:{and}\:{y}=\frac{\mathrm{2}}{\mathrm{2}+\frac{\mathrm{1}}{\mathrm{1}+{y}\:}}\:{find}\:{x}+{y} \\ $$

Question Number 89687 Answers: 1 Comments: 3

x^3 +x−16=0

$${x}^{\mathrm{3}} +{x}−\mathrm{16}=\mathrm{0} \\ $$

Question Number 89653 Answers: 1 Comments: 4

Question Number 89586 Answers: 1 Comments: 0

2018^(2019) −2019^(2018 ) ≡? (mod 4)

$$ \\ $$$$\mathrm{2018}^{\mathrm{2019}} −\mathrm{2019}^{\mathrm{2018}\:} \equiv?\:\left({mod}\:\mathrm{4}\right) \\ $$

Question Number 89505 Answers: 1 Comments: 0

Question Number 89454 Answers: 0 Comments: 1

Question Number 89592 Answers: 1 Comments: 2

cos(x)=k {−1≤k<0}

$${cos}\left({x}\right)={k}\: \\ $$$$\left\{−\mathrm{1}\leqslant{k}<\mathrm{0}\right\} \\ $$

Question Number 89385 Answers: 1 Comments: 1

Question Number 89344 Answers: 0 Comments: 6

(2x−1)^2 +8(√(2xy)) = 4 4y−(√(8xy−1)) = 1

$$\left(\mathrm{2}{x}−\mathrm{1}\right)^{\mathrm{2}} +\mathrm{8}\sqrt{\mathrm{2}{xy}}\:=\:\mathrm{4} \\ $$$$\mathrm{4}{y}−\sqrt{\mathrm{8}{xy}−\mathrm{1}}\:=\:\mathrm{1} \\ $$

Question Number 89300 Answers: 1 Comments: 4

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