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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 191651 Answers: 2 Comments: 1

Question Number 191582 Answers: 1 Comments: 0

f(x)=x^n . find A=f(1)+((f^′ (1))/1)+((f^(′′) (1))/2)+((f^(′′′) (1))/3)+...+((f^((n)) (1))/n)

$$\:\:{f}\left({x}\right)={x}^{{n}} \:.\:\:{find}\: \\ $$$$\:\:\:{A}={f}\left(\mathrm{1}\right)+\frac{{f}^{'} \left(\mathrm{1}\right)}{\mathrm{1}}+\frac{{f}^{''} \left(\mathrm{1}\right)}{\mathrm{2}}+\frac{{f}^{'''} \left(\mathrm{1}\right)}{\mathrm{3}}+...+\frac{{f}^{\left({n}\right)} \left(\mathrm{1}\right)}{{n}} \\ $$

Question Number 191579 Answers: 2 Comments: 0

f(x)=∣x∣ f^(−1) (x)=? solution?

$$\mathrm{f}\left(\mathrm{x}\right)=\mid\mathrm{x}\mid \\ $$$$\mathrm{f}^{−\mathrm{1}} \left(\mathrm{x}\right)=? \\ $$$$\mathrm{solution}? \\ $$

Question Number 191577 Answers: 0 Comments: 0

Give A′B′//AB, B′C′//BC and A′C′//AC Prove that: △ABC∽△A′B′C′

$${Give}\:{A}'{B}'//{AB},\:{B}'{C}'//{BC}\:{and}\:{A}'{C}'//{AC} \\ $$$${Prove}\:{that}:\:\bigtriangleup{ABC}\backsim\bigtriangleup{A}'{B}'{C}' \\ $$

Question Number 191569 Answers: 0 Comments: 0

Question Number 191568 Answers: 0 Comments: 0

Σ_(n=1) ^∞ (((−1)^n (x+1)^n )/((n+1)ln(n+1)))

$$\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{\left(−\mathrm{1}\right)^{{n}} \left({x}+\mathrm{1}\right)^{{n}} }{\left({n}+\mathrm{1}\right){ln}\left({n}+\mathrm{1}\right)} \\ $$

Question Number 191567 Answers: 1 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 191549 Answers: 0 Comments: 0

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 191528 Answers: 1 Comments: 0

find the value of the following series . Ω= Σ_(n=1) ^∞ (( cos(((nπ)/4) ))/n^( 2) ) =?

$$ \\ $$$$\:\:\:\:\:\:{find}\:\:{the}\:\:{value}\:\:{of}\:\:{the} \\ $$$$\:\:\:\:\:\:\:{following}\:\:{series}\:. \\ $$$$ \\ $$$$\:\:\:\:\:\:\:\:\Omega=\:\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{\:{cos}\left(\frac{{n}\pi}{\mathrm{4}}\:\right)}{{n}^{\:\mathrm{2}} }\:=? \\ $$

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 191519 Answers: 1 Comments: 0

∫_0 ^( (π/2)) (dx/(1+ sin x))

$$\int_{\mathrm{0}} ^{\:\frac{\pi}{\mathrm{2}}} \:\frac{{dx}}{\mathrm{1}+\:\mathrm{sin}\:{x}} \\ $$

Question Number 191518 Answers: 0 Comments: 1

Question Number 191602 Answers: 1 Comments: 1

Question Number 191597 Answers: 0 Comments: 0

Prove H_x → cot ( x ) x!→ sin ( x )

$${Prove} \\ $$$$ \\ $$$$\mathrm{H}_{{x}} \:\rightarrow\:\mathrm{cot}\:\left(\:\mathrm{x}\:\right)\: \\ $$$$\mathrm{x}!\rightarrow\:\:\mathrm{sin}\:\left(\:\mathrm{x}\:\right) \\ $$

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 191611 Answers: 1 Comments: 0

if x^2 −x+1 = 0 and α and β are thd roots of this equation then evaluate ((α^(100) +β^(100) )/(α^(100) −β^(100) ))

$${if}\:{x}^{\mathrm{2}} −{x}+\mathrm{1}\:=\:\mathrm{0}\:{and}\:\alpha\:{and}\:\beta\:{are}\:{thd}\:{roots} \\ $$$${of}\:{this}\:{equation}\:{then}\:{evaluate}\:\frac{\alpha^{\mathrm{100}} +\beta^{\mathrm{100}} }{\alpha^{\mathrm{100}} −\beta^{\mathrm{100}} } \\ $$

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