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write without roots in denominator if possible (1) (1/(√a)) (2) (1/((√a)+(√b))) (3) (1/((√a)+(√b)+(√c))) (4) (1/((√a)+(√b)+(√c)+(√d))) (5) (1/((√a)+(√b)+(√c)+(√d)+(√e)))

$$\mathrm{write}\:\mathrm{without}\:\mathrm{roots}\:\mathrm{in}\:\mathrm{denominator}\:\mathrm{if}\:\mathrm{possible} \\ $$$$\left(\mathrm{1}\right)\:\frac{\mathrm{1}}{\sqrt{{a}}} \\ $$$$\left(\mathrm{2}\right)\:\frac{\mathrm{1}}{\sqrt{{a}}+\sqrt{{b}}} \\ $$$$\left(\mathrm{3}\right)\:\frac{\mathrm{1}}{\sqrt{{a}}+\sqrt{{b}}+\sqrt{{c}}} \\ $$$$\left(\mathrm{4}\right)\:\frac{\mathrm{1}}{\sqrt{{a}}+\sqrt{{b}}+\sqrt{{c}}+\sqrt{{d}}} \\ $$$$\left(\mathrm{5}\right)\:\frac{\mathrm{1}}{\sqrt{{a}}+\sqrt{{b}}+\sqrt{{c}}+\sqrt{{d}}+\sqrt{{e}}} \\ $$

Question Number 58529 Answers: 3 Comments: 4

Solve for x and y (1/x) + (1/y) = 4 ....... (i) (x^2 /y) + (y^2 /x) = 9 ....... (ii)

$$\mathrm{Solve}\:\mathrm{for}\:\mathrm{x}\:\mathrm{and}\:\mathrm{y} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\frac{\mathrm{1}}{\mathrm{x}}\:+\:\frac{\mathrm{1}}{\mathrm{y}}\:=\:\mathrm{4}\:\:\:\:\:\:\:.......\:\left(\mathrm{i}\right) \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\frac{\mathrm{x}^{\mathrm{2}} }{\mathrm{y}}\:+\:\frac{\mathrm{y}^{\mathrm{2}} }{\mathrm{x}}\:\:=\:\:\mathrm{9}\:\:\:\:\:\:.......\:\left(\mathrm{ii}\right) \\ $$

Question Number 58248 Answers: 1 Comments: 0

leg A_1 ,A_2 ,...A_n and H_1 ,H_2 ,...H_n are n A.M′S and H.M′S respectively between a and b prove that A_r H_(n−r+1) =ab n≥r≥1

$${leg}\:{A}_{\mathrm{1}} ,{A}_{\mathrm{2}} ,...{A}_{{n}} \:{and}\:{H}_{\mathrm{1}} ,{H}_{\mathrm{2}} ,...{H}_{{n}} \:{are}\:{n}\:{A}.{M}'{S}\: \\ $$$${and}\:{H}.{M}'{S}\:{respectively}\:{between}\:{a}\:{and}\:{b} \\ $$$${prove}\:{that}\:{A}_{{r}} {H}_{{n}−{r}+\mathrm{1}} ={ab} \\ $$$$\:{n}\geqslant{r}\geqslant\mathrm{1} \\ $$

Question Number 58246 Answers: 1 Comments: 0

show that P=x^(9999) +x^(8888) +x^(7777) +x^(6666) +x^(5555) +x^(4444) +x^(3333) +x^(2222) +x^(1111) +1 Q=x^9 +x^8 +x^7 +x^6 +x^5 +x^4 +x^3 +x^2 +x+1 prove P is divisible by Q

$${show}\:{that} \\ $$$${P}={x}^{\mathrm{9999}} +{x}^{\mathrm{8888}} +{x}^{\mathrm{7777}} +{x}^{\mathrm{6666}} +{x}^{\mathrm{5555}} +{x}^{\mathrm{4444}} +{x}^{\mathrm{3333}} +{x}^{\mathrm{2222}} +{x}^{\mathrm{1111}} +\mathrm{1} \\ $$$${Q}={x}^{\mathrm{9}} +{x}^{\mathrm{8}} +{x}^{\mathrm{7}} +{x}^{\mathrm{6}} +{x}^{\mathrm{5}} +{x}^{\mathrm{4}} +{x}^{\mathrm{3}} +{x}^{\mathrm{2}} +{x}+\mathrm{1} \\ $$$${prove}\:\:{P}\:\:{is}\:{divisible}\:{by}\:{Q} \\ $$

Question Number 58210 Answers: 0 Comments: 5

find two possible number such that 1) xy=(x/y)=x−y 2)xy=((2x)/y)=3(x−y) 3) xy=(x/y)=2(x−y).

$$\mathrm{find}\:\mathrm{two}\:\mathrm{possible}\:\mathrm{number}\:\mathrm{such}\:\mathrm{that} \\ $$$$\left.\mathrm{1}\right)\:\:\mathrm{xy}=\frac{\mathrm{x}}{\mathrm{y}}=\mathrm{x}−\mathrm{y} \\ $$$$\left.\mathrm{2}\right)\mathrm{xy}=\frac{\mathrm{2x}}{\mathrm{y}}=\mathrm{3}\left(\mathrm{x}−\mathrm{y}\right) \\ $$$$\left.\mathrm{3}\right)\:\:\mathrm{xy}=\frac{\mathrm{x}}{\mathrm{y}}=\mathrm{2}\left(\mathrm{x}−\mathrm{y}\right). \\ $$$$ \\ $$$$ \\ $$$$ \\ $$$$ \\ $$$$ \\ $$

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