Question and Answers Forum

AlgebraQuestion and Answers: Page 64

Question Number 191614 Answers: 0 Comments: 1

((α^(100) +β^(100) )/(α^(100) −β^(100) )) = (((−w)^(100) +(−w^2 )^(100) )/((−w)^(100) −(−w^2 )^(100) )) = ((w^(100) +w^(200) )/(w^(100) −w^(200) )) = ((1+w^(100) )/(1−w^(100 ) )) = ((1+w)/(1−w)) = (2/(2w)) = (1/w) =

$$\frac{\alpha^{\mathrm{100}} +\beta^{\mathrm{100}} }{\alpha^{\mathrm{100}} −\beta^{\mathrm{100}} }\:=\: \\ $$$$\frac{\left(−{w}\right)^{\mathrm{100}} +\left(−{w}^{\mathrm{2}} \right)^{\mathrm{100}} }{\left(−{w}\right)^{\mathrm{100}} −\left(−{w}^{\mathrm{2}} \right)^{\mathrm{100}} } \\ $$$$=\:\frac{{w}^{\mathrm{100}} +{w}^{\mathrm{200}} }{{w}^{\mathrm{100}} −{w}^{\mathrm{200}} } \\ $$$$=\:\frac{\mathrm{1}+{w}^{\mathrm{100}} }{\mathrm{1}−{w}^{\mathrm{100}\:} } \\ $$$$=\:\frac{\mathrm{1}+{w}}{\mathrm{1}−{w}}\:=\:\frac{\mathrm{2}}{\mathrm{2}{w}}\:=\:\frac{\mathrm{1}}{{w}}\:=\: \\ $$

Question Number 191610 Answers: 1 Comments: 0

Q: if x+(1/x)=2cos(θ) prove it x^n +(1/x^n )=2cos(nθ)

$${Q}:\:{if}\:\:{x}+\frac{\mathrm{1}}{{x}}=\mathrm{2}{cos}\left(\theta\right)\:\:{prove}\:{it}\:\:{x}^{{n}} +\frac{\mathrm{1}}{{x}^{{n}} }=\mathrm{2}{cos}\left({n}\theta\right) \\ $$

Question Number 191589 Answers: 1 Comments: 1

a^x = bc, b^y = ca, c^z = ab. Prove that, (x/(1 + x)) + (y/(1 + y)) + (z/(1 + z)) = 2. (Without using log) a ≠ b ≠ c

$${a}^{{x}} \:=\:{bc},\:{b}^{{y}} \:=\:{ca},\:{c}^{{z}} \:=\:{ab}. \\ $$$$\mathrm{Prove}\:\mathrm{that},\:\frac{{x}}{\mathrm{1}\:+\:{x}}\:+\:\frac{{y}}{\mathrm{1}\:+\:{y}}\:+\:\frac{{z}}{\mathrm{1}\:+\:{z}}\:=\:\mathrm{2}. \\ $$$$\left(\mathrm{Without}\:\mathrm{using}\:\mathrm{log}\right) \\ $$$${a}\:\neq\:{b}\:\neq\:{c} \\ $$

Question Number 191569 Answers: 0 Comments: 0

Question Number 191555 Answers: 0 Comments: 1

Solve (√x) + y = 11 x + (√y) = 7

$$\mathrm{Solve} \\ $$$$\sqrt{{x}}\:+\:{y}\:=\:\mathrm{11} \\ $$$${x}\:+\:\sqrt{{y}}\:=\:\mathrm{7} \\ $$

Question Number 191553 Answers: 4 Comments: 1

If a^2 + a + 1 = 0 then find a^5 + a^4 + 1.

$$\mathrm{If}\:{a}^{\mathrm{2}} \:+\:{a}\:+\:\mathrm{1}\:=\:\mathrm{0}\:\mathrm{then}\:\mathrm{find}\:{a}^{\mathrm{5}} \:+\:{a}^{\mathrm{4}} \:+\:\mathrm{1}. \\ $$

Question Number 191552 Answers: 2 Comments: 0

If x^2 − 3x + 1 = 0 then find the value of (x^2 + x + (1/x) + (1/x^2 ))^2

$$\mathrm{If}\:{x}^{\mathrm{2}} \:−\:\mathrm{3}{x}\:+\:\mathrm{1}\:=\:\mathrm{0}\:\mathrm{then}\:\mathrm{find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of} \\ $$$$\left({x}^{\mathrm{2}} \:+\:{x}\:+\:\frac{\mathrm{1}}{{x}}\:+\:\frac{\mathrm{1}}{{x}^{\mathrm{2}} }\right)^{\mathrm{2}} \\ $$

Question Number 191546 Answers: 1 Comments: 0

If m + 1 = (√n) + 3 then find the value of (1/2)(((m^3 − 6m^2 + 12m −8)/( (√n))) − n)

$$\mathrm{If}\:{m}\:+\:\mathrm{1}\:=\:\sqrt{{n}}\:+\:\mathrm{3}\:\mathrm{then}\:\mathrm{find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of} \\ $$$$\frac{\mathrm{1}}{\mathrm{2}}\left(\frac{{m}^{\mathrm{3}} \:−\:\mathrm{6}{m}^{\mathrm{2}} \:+\:\mathrm{12}{m}\:−\mathrm{8}}{\:\sqrt{{n}}}\:−\:{n}\right) \\ $$

Question Number 191536 Answers: 2 Comments: 0

Factorize (2/(2x − 1)) −5 + (3/(3x − 1))

$$\mathrm{Factorize} \\ $$$$\frac{\mathrm{2}}{\mathrm{2}{x}\:−\:\mathrm{1}}\:−\mathrm{5}\:+\:\frac{\mathrm{3}}{\mathrm{3}{x}\:−\:\mathrm{1}} \\ $$

Question Number 191530 Answers: 0 Comments: 3

Question Number 191529 Answers: 2 Comments: 0

If ((x − y)/(x(√y) + y(√x))) = (1/( (√x))) ; (x > 0 and y > 0) then Find the value of (x/y) .

$$\mathrm{If}\:\frac{{x}\:−\:{y}}{{x}\sqrt{{y}}\:+\:{y}\sqrt{{x}}}\:=\:\frac{\mathrm{1}}{\:\sqrt{{x}}}\:;\:\left({x}\:>\:\mathrm{0}\:\mathrm{and}\:{y}\:>\:\mathrm{0}\right)\:\mathrm{then} \\ $$$$\mathrm{Find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\frac{{x}}{{y}}\:. \\ $$

Question Number 191527 Answers: 2 Comments: 0

x + y = 1 and x^2 + y^2 = 2. Find the value of x^(11) + y^(11) .

$${x}\:+\:{y}\:=\:\mathrm{1}\:\mathrm{and}\:{x}^{\mathrm{2}} \:+\:{y}^{\mathrm{2}} \:=\:\mathrm{2}.\:\mathrm{Find}\:\mathrm{the}\:\mathrm{value} \\ $$$$\mathrm{of}\:{x}^{\mathrm{11}} \:+\:{y}^{\mathrm{11}} . \\ $$

Question Number 191525 Answers: 1 Comments: 0

Q : Show that the numbers (√(3 )) , 2 & (√8) cannot be terms of an arithmetic sequence.

$${Q}\::\:{Show}\:{that}\:{the}\:{numbers}\:\sqrt{\mathrm{3}\:}\:,\:\mathrm{2}\:\&\:\sqrt{\mathrm{8}}\:{cannot}\:{be}\:{terms}\:{of}\:{an}\:{arithmetic}\:{sequence}. \\ $$

Question Number 191595 Answers: 1 Comments: 0

a = ((xy)/(x + y)) , b = ((xz)/(x + z)) and c = ((yz)/(y + z)) . Represent x in a, b, c form. [x, y, z ≠ 0]

$${a}\:=\:\frac{{xy}}{{x}\:+\:{y}}\:,\:{b}\:=\:\frac{{xz}}{{x}\:+\:{z}}\:\mathrm{and}\:{c}\:=\:\frac{{yz}}{{y}\:+\:{z}}\:. \\ $$$$\mathrm{Represent}\:{x}\:\mathrm{in}\:{a},\:{b},\:{c}\:\mathrm{form}.\:\left[{x},\:{y},\:{z}\:\neq\:\mathrm{0}\right] \\ $$

Question Number 191512 Answers: 1 Comments: 0

Q: the equation ⌊ cos(4x )⌋=m.cos(2x) has no solution . x∈ (0, (π/2) ) find the acceptable real values for ”m”.

$$ \\ $$$$\:\:\:\:\:{Q}:\:\:\:\:\:\:\:{the}\:{equation}\: \\ $$$$\:\:\:\: \\ $$$$\:\:\:\lfloor\:\mathrm{cos}\left(\mathrm{4}{x}\:\right)\rfloor={m}.\mathrm{cos}\left(\mathrm{2}{x}\right) \\ $$$$\:\:\:{has}\:{no}\:\:{solution}\:.\:\:{x}\in\:\left(\mathrm{0},\:\frac{\pi}{\mathrm{2}}\:\right) \\ $$$$\:\:\:\:{find}\:{the}\:{acceptable} \\ $$$$\:\:\:\:\:\:\:{real}\:{values}\:{for}\:\:\:\:''{m}''. \\ $$

Question Number 191508 Answers: 0 Comments: 0

Question Number 191486 Answers: 1 Comments: 0

a(√a) + b(√b) = 183 and b(√a) + a(√b) = 182 What is the value of (9/5) (a + b) ?

$${a}\sqrt{{a}}\:+\:{b}\sqrt{{b}}\:=\:\mathrm{183}\:\mathrm{and}\:{b}\sqrt{{a}}\:+\:{a}\sqrt{{b}}\:=\:\mathrm{182} \\ $$$$\mathrm{What}\:\mathrm{is}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\frac{\mathrm{9}}{\mathrm{5}}\:\left({a}\:+\:{b}\right)\:? \\ $$

Question Number 191473 Answers: 0 Comments: 0

Question Number 191456 Answers: 0 Comments: 0

Question Number 191454 Answers: 1 Comments: 2

Question Number 191451 Answers: 1 Comments: 0

x+(1/x)=5 and x∙y=4 find x^2 +((1/y))^2 =?

$${x}+\frac{\mathrm{1}}{{x}}=\mathrm{5}\:\:{and}\:{x}\centerdot{y}=\mathrm{4}\:{find} \\ $$$${x}^{\mathrm{2}} +\left(\frac{\mathrm{1}}{{y}}\right)^{\mathrm{2}} =? \\ $$

Question Number 191450 Answers: 0 Comments: 0

x+(1/x)=5 and x∙y=4 faind x^4 +((1/y))^3 =?

$${x}+\frac{\mathrm{1}}{{x}}=\mathrm{5}\:\:{and}\:\:{x}\centerdot{y}=\mathrm{4} \\ $$$${faind}\:\:\:\:{x}^{\mathrm{4}} +\left(\frac{\mathrm{1}}{{y}}\right)^{\mathrm{3}} =? \\ $$

Question Number 191445 Answers: 0 Comments: 0

Factorize (x − 998)(x − 999)−(((1000)/(999^2 )))

$$\mathrm{Factorize} \\ $$$$\left({x}\:−\:\mathrm{998}\right)\left({x}\:−\:\mathrm{999}\right)−\left(\frac{\mathrm{1000}}{\mathrm{999}^{\mathrm{2}} }\right) \\ $$

Question Number 191443 Answers: 2 Comments: 0

(3^(100) + 2^(100) ), 4^(100) which is greater? Give proof.

$$\left(\mathrm{3}^{\mathrm{100}} \:+\:\mathrm{2}^{\mathrm{100}} \right),\:\mathrm{4}^{\mathrm{100}} \:\mathrm{which}\:\mathrm{is}\:\mathrm{greater}? \\ $$$$\mathrm{Give}\:\mathrm{proof}. \\ $$

Question Number 191442 Answers: 0 Comments: 0

Question Number 191440 Answers: 0 Comments: 0

Pg 59 Pg 60 Pg 61 Pg 62 Pg 63 Pg 64 Pg 65 Pg 66 Pg 67 Pg 68

Contact: info@tinkutara.com