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Question Number 96021 Answers: 0 Comments: 1

if p and q are two complex number and p×q=m ,m is a real number . is there always exists a p^(1/3) and q^(1/3) (we know p^(1/3) and q^(1/3) each has actually 3 values) such that p^(1/3) ×q^(1/3) =m^(1/3) .where m^(1/3) is real .?? how to prove it?

Question Number 96012 Answers: 2 Comments: 1

Question Number 96008 Answers: 0 Comments: 1

((1−(1/a))/(a^2 −(1/a^2 )))

$$\frac{\mathrm{1}−\frac{\mathrm{1}}{\mathrm{a}}}{\mathrm{a}^{\mathrm{2}} −\frac{\mathrm{1}}{\mathrm{a}^{\mathrm{2}} }} \\ $$

Question Number 96007 Answers: 0 Comments: 1

((9x^2 +4a^2 )/(9x^2 −4a^2 )) +((3x)/(3x+2a)) −((2a)/(2a−3x))

$$\frac{\mathrm{9x}^{\mathrm{2}} +\mathrm{4a}^{\mathrm{2}} }{\mathrm{9x}^{\mathrm{2}} −\mathrm{4a}^{\mathrm{2}} }\:+\frac{\mathrm{3x}}{\mathrm{3x}+\mathrm{2a}}\:−\frac{\mathrm{2a}}{\mathrm{2a}−\mathrm{3x}} \\ $$

Question Number 95999 Answers: 2 Comments: 0

Question Number 95986 Answers: 0 Comments: 1

In a set of 3 consecutive natural numbers the sum of the last 2 numbers is equal to 3 times the first numbers. Find the sum of all the three numbers.

$$\mathrm{In}\:\mathrm{a}\:\mathrm{set}\:\mathrm{of}\:\mathrm{3}\:\mathrm{consecutive}\:\mathrm{natural}\:\mathrm{numbers} \\ $$$$\mathrm{the}\:\mathrm{sum}\:\mathrm{of}\:\mathrm{the}\:\mathrm{last}\:\mathrm{2}\:\mathrm{numbers}\:\mathrm{is}\:\mathrm{equal} \\ $$$$\mathrm{to}\:\mathrm{3}\:\mathrm{times}\:\mathrm{the}\:\mathrm{first}\:\mathrm{numbers}.\:\mathrm{Find}\:\mathrm{the} \\ $$$$\mathrm{sum}\:\mathrm{of}\:\mathrm{all}\:\mathrm{the}\:\mathrm{three}\:\mathrm{numbers}. \\ $$

Question Number 95985 Answers: 2 Comments: 0

A and B can complete a piece of work in 12 days and 24 days respectively. After A had worked for 6 days, B joined him, and then they completed the work. How much should A receive as his share from the total amount of Rs. 180 paid for completing the work?

$$\mathrm{A}\:\mathrm{and}\:\mathrm{B}\:\mathrm{can}\:\mathrm{complete}\:\mathrm{a}\:\mathrm{piece}\:\mathrm{of}\:\mathrm{work}\:\mathrm{in} \\ $$$$\mathrm{12}\:\mathrm{days}\:\mathrm{and}\:\mathrm{24}\:\mathrm{days}\:\mathrm{respectively}.\:\mathrm{After} \\ $$$$\mathrm{A}\:\mathrm{had}\:\mathrm{worked}\:\mathrm{for}\:\mathrm{6}\:\mathrm{days},\:\mathrm{B}\:\mathrm{joined}\:\mathrm{him}, \\ $$$$\mathrm{and}\:\mathrm{then}\:\mathrm{they}\:\mathrm{completed}\:\mathrm{the}\:\mathrm{work}.\:\mathrm{How} \\ $$$$\mathrm{much}\:\mathrm{should}\:\:\mathrm{A}\:\mathrm{receive}\:\mathrm{as}\:\mathrm{his}\:\mathrm{share}\:\mathrm{from} \\ $$$$\mathrm{the}\:\mathrm{total}\:\mathrm{amount}\:\mathrm{of}\:\mathrm{Rs}.\:\mathrm{180}\:\mathrm{paid}\:\mathrm{for} \\ $$$$\mathrm{completing}\:\mathrm{the}\:\mathrm{work}? \\ $$

Question Number 95982 Answers: 1 Comments: 0

Σx(y^3 −z^3 )=_____.

$$\Sigma{x}\left({y}^{\mathrm{3}} −{z}^{\mathrm{3}} \right)=\_\_\_\_\_. \\ $$

Question Number 95980 Answers: 1 Comments: 0

If lim_(x→3) (((√(3x+7))−((20x+4))^(1/(3 )) +ax+b)/((x−3)^2 )) exist , what is the value of ab

$$\mathrm{If}\:\underset{{x}\rightarrow\mathrm{3}} {\mathrm{lim}}\frac{\sqrt{\mathrm{3x}+\mathrm{7}}−\sqrt[{\mathrm{3}\:\:}]{\mathrm{20x}+\mathrm{4}}\:+{a}\mathrm{x}+{b}}{\left({x}−\mathrm{3}\right)^{\mathrm{2}} } \\ $$$$\mathrm{exist}\:,\:\mathrm{what}\:\mathrm{is}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:{ab}\: \\ $$

Question Number 95968 Answers: 1 Comments: 0

3^(((log _3 (2)+log _3 (3log _(1/3) (cot (π/3))))/(log _π (3).(log _2 (π)))) ? )

$$\mathrm{3}^{\frac{\mathrm{log}\:_{\mathrm{3}} \left(\mathrm{2}\right)+\mathrm{log}\:_{\mathrm{3}} \left(\mathrm{3log}\:_{\frac{\mathrm{1}}{\mathrm{3}}} \left(\mathrm{cot}\:\frac{\pi}{\mathrm{3}}\right)\right)}{\mathrm{log}\:_{\pi} \left(\mathrm{3}\right).\left(\mathrm{log}\:_{\mathrm{2}} \left(\pi\right)\right)}\:?\:} \\ $$

Question Number 95964 Answers: 0 Comments: 0

{ ((x^2 +y^2 =13)),((2x^2 +3y=2xy^2 )) :}