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Question Number 70385 Answers: 1 Comments: 0

The value of determinant determinant (((x+2),( x+3),(x+5)),((x+4),( x+6),(x+9)),((x+8),(x+11),(x+15))) is

$$\mathrm{The}\:\mathrm{value}\:\mathrm{of}\:\mathrm{determinant} \\ $$$$\begin{vmatrix}{{x}+\mathrm{2}}&{\:{x}+\mathrm{3}}&{{x}+\mathrm{5}}\\{{x}+\mathrm{4}}&{\:{x}+\mathrm{6}}&{{x}+\mathrm{9}}\\{{x}+\mathrm{8}}&{{x}+\mathrm{11}}&{{x}+\mathrm{15}}\end{vmatrix}\:\mathrm{is} \\ $$

Question Number 70383 Answers: 0 Comments: 1

If a matrix A is such that 3A^3 +2A^2 +5A+I=0, then A^(−1) is equal to

$$\mathrm{If}\:\mathrm{a}\:\mathrm{matrix}\:{A}\:\mathrm{is}\:\mathrm{such}\:\mathrm{that}\:\mathrm{3}{A}^{\mathrm{3}} +\mathrm{2}{A}^{\mathrm{2}} +\mathrm{5}{A}+{I}=\mathrm{0}, \\ $$$$\mathrm{then}\:{A}^{−\mathrm{1}} \mathrm{is}\:\mathrm{equal}\:\mathrm{to} \\ $$

Question Number 70399 Answers: 1 Comments: 3

Solve x^4 + x^3 −2ax^2 −ax + a^2 = 0, a ∈ R

$$\boldsymbol{{Solve}}\:\:\boldsymbol{{x}}^{\mathrm{4}} \:+\:\boldsymbol{{x}}^{\mathrm{3}} \:−\mathrm{2}\boldsymbol{{ax}}^{\mathrm{2}} \:−\boldsymbol{{ax}}\:+\:\boldsymbol{{a}}^{\mathrm{2}} =\:\mathrm{0},\:\:\boldsymbol{{a}}\:\in\:\mathbb{R} \\ $$

Question Number 70370 Answers: 1 Comments: 4

If gcd(p , q)=1,prove that gcd(p(p+q) , q(p+q) , pq)=1 Related to Q#69939

$${If}\:\:{gcd}\left({p}\:,\:{q}\right)=\mathrm{1},{prove}\:{that} \\ $$$$\:\:\:\:\:{gcd}\left({p}\left({p}+{q}\right)\:,\:{q}\left({p}+{q}\right)\:,\:{pq}\right)=\mathrm{1} \\ $$$$\mathrm{R}\boldsymbol{\mathrm{elated}}\:\boldsymbol{\mathrm{to}}\:\boldsymbol{\mathrm{Q}}#\mathrm{69939} \\ $$

Question Number 70369 Answers: 0 Comments: 1

Question Number 70361 Answers: 0 Comments: 0

Hello si(x)=−∫_x ^∞ ((sin(x))/x)dx show ∫_0 ^(+∞) x^(a−1) si(x)dx=−((Γ(a)sin(((πa)/2)))/a) hint ipp +complex Analysis

$${Hello}\: \\ $$$${si}\left({x}\right)=−\int_{{x}} ^{\infty} \frac{{sin}\left({x}\right)}{{x}}{dx} \\ $$$${show}\:\int_{\mathrm{0}} ^{+\infty} {x}^{{a}−\mathrm{1}} {si}\left({x}\right){dx}=−\frac{\Gamma\left({a}\right){sin}\left(\frac{\pi{a}}{\mathrm{2}}\right)}{{a}} \\ $$$${hint}\:{ipp}\:+{complex}\:{Analysis} \\ $$

Question Number 70312 Answers: 1 Comments: 1

If, (1/a^2 )+(1/b^2 )+(1/c^2 ) = (1/(ab))+(1/(bc))+(1/(ca)) then prove that, a=b=c.

$$\mathrm{If},\:\frac{\mathrm{1}}{\mathrm{a}^{\mathrm{2}} }+\frac{\mathrm{1}}{\mathrm{b}^{\mathrm{2}} }+\frac{\mathrm{1}}{\mathrm{c}^{\mathrm{2}} }\:=\:\frac{\mathrm{1}}{\mathrm{ab}}+\frac{\mathrm{1}}{\mathrm{bc}}+\frac{\mathrm{1}}{\mathrm{ca}}\:\mathrm{then}\:\mathrm{prove}\: \\ $$$$\mathrm{that},\:\mathrm{a}=\mathrm{b}=\mathrm{c}. \\ $$

Question Number 70364 Answers: 0 Comments: 3

solve L=lim_(x→0) ((e^x −(1/(1−x)))/x^2 )

$$\mathrm{solve}\:\mathrm{L}=\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{\mathrm{e}^{\mathrm{x}} −\frac{\mathrm{1}}{\mathrm{1}−\mathrm{x}}}{\mathrm{x}^{\mathrm{2}} } \\ $$

Question Number 70310 Answers: 3 Comments: 1

please help me find the term independent of x in the expansion of (x + (3/x))^(−12 )

$${please}\:{help}\:{me}\:{find}\:{the}\:{term}\:{independent}\:{of}\:{x} \\ $$$${in}\:{the}\:{expansion}\:{of}\: \\ $$$$\:\:\:\:\:\:\left({x}\:+\:\frac{\mathrm{3}}{{x}}\right)^{−\mathrm{12}\:} \\ $$

Question Number 70277 Answers: 2 Comments: 0

Question Number 70270 Answers: 1 Comments: 0

If log_x y = 6 & log_(14x) 8y = 3 then find the value of x & y.

$$\mathrm{If}\:\mathrm{log}_{\mathrm{x}} \mathrm{y}\:=\:\mathrm{6}\:\&\:\mathrm{log}_{\mathrm{14x}} \mathrm{8y}\:=\:\mathrm{3}\:\mathrm{then}\:\mathrm{find}\:\mathrm{the} \\ $$$$\mathrm{value}\:\mathrm{of}\:\mathrm{x}\:\&\:\mathrm{y}. \\ $$

Question Number 70262 Answers: 0 Comments: 1

calculate ∫_0 ^(π/4) ln(cosx)dx and ∫_0 ^(π/4) ln(sinx)dx

$${calculate}\:\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{4}}} {ln}\left({cosx}\right){dx}\:\:{and}\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{4}}} {ln}\left({sinx}\right){dx} \\ $$

Question Number 70256 Answers: 0 Comments: 1

Question Number 70253 Answers: 0 Comments: 3

Question Number 70252 Answers: 1 Comments: 0

If, log x^y = 6 and log 14x^(8y) = 3 then find the value of x, y.

$$\mathrm{If},\:\mathrm{log}\:\mathrm{x}^{\mathrm{y}} \:=\:\mathrm{6}\:\mathrm{and}\:\mathrm{log}\:\mathrm{14x}^{\mathrm{8y}} \:=\:\mathrm{3}\:\mathrm{then}\:\mathrm{find} \\ $$$$\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\mathrm{x},\:\mathrm{y}. \\ $$

Question Number 70287 Answers: 0 Comments: 2

I wanted to say this earlier... I love mathematics and I also love people. But I′m not here to solve the same old boring problems copied from facebook or whatsapp or other platforms. They are not interesting at all. They have been coming in as a kind of competition, or simply to brag, they′ve been traded from one non−mathematician to the other. No use to copy−paste problems that you found somewhere on the web and that you might not even be able to fully understand. If you need an explanation, you′re welcome, but I won′t do your homework and I won′t answer impolite posts. Last but not least: I won′t try to solve the famous unsolved problems much better people were not able to cope with.

Question Number 70232 Answers: 0 Comments: 3

Solve xy′ − y sin x + y^5 = 0

$$\mathrm{Solve} \\ $$$${xy}'\:−\:{y}\:\mathrm{sin}\:{x}\:+\:{y}^{\mathrm{5}} \:=\:\mathrm{0} \\ $$

Question Number 70230 Answers: 0 Comments: 2