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AlgebraQuestion and Answers: Page 348

Question Number 12361 Answers: 1 Comments: 0

((√2) +(√3) +2 + (√5))(−(√2) + (√3) + 2 − (√5))((√(10)) + 2(√3)) Can you solve this without solving them manually?

$$\left(\sqrt{\mathrm{2}}\:+\sqrt{\mathrm{3}}\:+\mathrm{2}\:+\:\sqrt{\mathrm{5}}\right)\left(−\sqrt{\mathrm{2}}\:+\:\sqrt{\mathrm{3}}\:+\:\mathrm{2}\:−\:\sqrt{\mathrm{5}}\right)\left(\sqrt{\mathrm{10}}\:+\:\mathrm{2}\sqrt{\mathrm{3}}\right) \\ $$$$ \\ $$$$\mathrm{Can}\:\mathrm{you}\:\mathrm{solve}\:\mathrm{this}\:\mathrm{without}\:\mathrm{solving}\:\mathrm{them}\:\mathrm{manually}? \\ $$

Question Number 12359 Answers: 1 Comments: 0

Question Number 12292 Answers: 2 Comments: 0

Question Number 12261 Answers: 1 Comments: 0

find the value of a b and c a+b+c=4 a^2 +b^2 +c^2 =66 a^3 +b^3 +c^3 =280

$${find}\:{the}\:{value}\:{of}\:{a}\:{b}\:{and}\:{c} \\ $$$$\:{a}+{b}+{c}=\mathrm{4} \\ $$$${a}^{\mathrm{2}} +{b}^{\mathrm{2}} +{c}^{\mathrm{2}} =\mathrm{66} \\ $$$${a}^{\mathrm{3}} +{b}^{\mathrm{3}} +{c}^{\mathrm{3}} =\mathrm{280} \\ $$

Question Number 12257 Answers: 1 Comments: 0

Question Number 12255 Answers: 2 Comments: 0

Question Number 12254 Answers: 0 Comments: 0

Question Number 12197 Answers: 0 Comments: 8

Question Number 12171 Answers: 1 Comments: 0

∫x^2 ×sgn(2x)dx=?

$$\int\mathrm{x}^{\mathrm{2}} ×\mathrm{sgn}\left(\mathrm{2x}\right)\mathrm{dx}=? \\ $$

Question Number 12161 Answers: 0 Comments: 2

Question Number 12144 Answers: 1 Comments: 0

(1/(1+1^2 +1^4 ))+(2/(1+2^2 +2^4 ))+(3/(1+3^2 +3^4 ))+.....∞=?

$$\frac{\mathrm{1}}{\mathrm{1}+\mathrm{1}^{\mathrm{2}} +\mathrm{1}^{\mathrm{4}} }+\frac{\mathrm{2}}{\mathrm{1}+\mathrm{2}^{\mathrm{2}} +\mathrm{2}^{\mathrm{4}} }+\frac{\mathrm{3}}{\mathrm{1}+\mathrm{3}^{\mathrm{2}} +\mathrm{3}^{\mathrm{4}} }+.....\infty=? \\ $$

Question Number 12126 Answers: 1 Comments: 0

Question Number 12111 Answers: 0 Comments: 0

show that: Σ_(n=0) ^∞ (((−1)^n )/(n!))=(1/e) please show your working

$$\mathrm{show}\:\mathrm{that}: \\ $$$$\underset{{n}=\mathrm{0}} {\overset{\infty} {\sum}}\frac{\left(−\mathrm{1}\right)^{{n}} }{{n}!}=\frac{\mathrm{1}}{{e}} \\ $$$$\mathrm{please}\:\mathrm{show}\:\mathrm{your}\:\mathrm{working} \\ $$

Question Number 12109 Answers: 0 Comments: 0

show that: Σ_(n=1) ^∞ (((−1)^(n+1) )/n)=ln(2) please show your working

$$\mathrm{show}\:\mathrm{that}: \\ $$$$\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{\left(−\mathrm{1}\right)^{{n}+\mathrm{1}} }{{n}}=\mathrm{ln}\left(\mathrm{2}\right) \\ $$$$\mathrm{please}\:\mathrm{show}\:\mathrm{your}\:\mathrm{working} \\ $$

Question Number 12096 Answers: 1 Comments: 0

Question Number 12093 Answers: 1 Comments: 0

log_(abc) b=3 log_(abc) c=4 log_(abc) a=?

$$\mathrm{log}_{\mathrm{abc}} \mathrm{b}=\mathrm{3} \\ $$$$\mathrm{log}_{\mathrm{abc}} \mathrm{c}=\mathrm{4} \\ $$$$\mathrm{log}_{\mathrm{abc}} \mathrm{a}=? \\ $$

Question Number 12080 Answers: 1 Comments: 0

Question Number 12074 Answers: 1 Comments: 0

Question Number 12030 Answers: 1 Comments: 0

Question Number 12017 Answers: 0 Comments: 0

How Can we expand (a+b)^(1/2) and (a+b)^(−n) ?

$${How}\:{Can}\:{we}\:{expand}\:\left({a}+{b}\right)^{\frac{\mathrm{1}}{\mathrm{2}}} \:{and} \\ $$$$\left({a}+{b}\right)^{−{n}} \:? \\ $$

Question Number 11914 Answers: 0 Comments: 0

Turevlenebilir bir f fonksiyonu icin f(x+y)=f(x)+f(y)+2xy ve f′(0)=−3 old.gore f′(2)=? czm∵ f(x+y)=f(x)+f(y)+2xy y yi sabit kabul edersek f′(x+y)=f′(x)+2y x=0,y=2 icn f′(2)=f′(0)+2.2 f′(2)=−3+4=1

$${Turevlenebilir}\:{bir}\:{f}\:{fonksiyonu}\:{icin} \\ $$$${f}\left({x}+{y}\right)={f}\left({x}\right)+{f}\left({y}\right)+\mathrm{2}{xy}\:{ve}\:{f}'\left(\mathrm{0}\right)=−\mathrm{3} \\ $$$${old}.{gore}\:{f}'\left(\mathrm{2}\right)=? \\ $$$${czm}\because\:\:{f}\left({x}+{y}\right)={f}\left({x}\right)+{f}\left({y}\right)+\mathrm{2}{xy} \\ $$$${y}\:{yi}\:{sabit}\:{kabul}\:{edersek} \\ $$$${f}'\left({x}+{y}\right)={f}'\left({x}\right)+\mathrm{2}{y} \\ $$$${x}=\mathrm{0},{y}=\mathrm{2}\:{icn} \\ $$$${f}'\left(\mathrm{2}\right)={f}'\left(\mathrm{0}\right)+\mathrm{2}.\mathrm{2} \\ $$$${f}'\left(\mathrm{2}\right)=−\mathrm{3}+\mathrm{4}=\mathrm{1} \\ $$

Question Number 11901 Answers: 0 Comments: 0

((7cos^2 x+sin^2 x−3)/(2cos^2 x−sin^2 x))=? czm∵ ((7cos^2 x+1−cos^2 x−3)/(2cos^2 x−sin^2 x)) ((6cos^2 x−2)/(2cos^2 x−(1−cos^2 x)))=((6cos^2 x−2)/(3cos^2 x−1)) ((2(3cos^2 x−1))/(3cos^2 x−1))=2

Question Number 11869 Answers: 0 Comments: 0

Why the expansion of (a+b)^(−n) follows newton′s expansion rule?

$${Why}\:{the}\:{expansion}\:{of}\:\:\left({a}+{b}\right)^{−{n}} \:{follows} \\ $$$${newton}'{s}\:{expansion}\:{rule}? \\ $$

Question Number 11831 Answers: 0 Comments: 0

the system of equation a − (√(c^2 −(1/(16)) ))= (√(b^2 − (1/(16)))) b − (√(a^2 − (1/(25))))= (√(c^2 − (1/(25)))) c − (√(b^2 − (1/(36))))= (√(a^2 − (1/(36)))) given that a, b, c are real numbers that satisfy they system of equation ... if a + b + c = (x/(√(y ))) where x, y are positive integers and y is square free find the value of x + y

$$\mathrm{the}\:\mathrm{system}\:\mathrm{of}\:\mathrm{equation} \\ $$$$ \\ $$$$\mathrm{a}\:−\:\sqrt{\mathrm{c}^{\mathrm{2}} \:−\frac{\mathrm{1}}{\mathrm{16}}\:}=\:\sqrt{\mathrm{b}^{\mathrm{2}} \:−\:\frac{\mathrm{1}}{\mathrm{16}}} \\ $$$$\mathrm{b}\:−\:\sqrt{\mathrm{a}^{\mathrm{2}} \:−\:\frac{\mathrm{1}}{\mathrm{25}}}=\:\sqrt{\mathrm{c}^{\mathrm{2}} \:−\:\frac{\mathrm{1}}{\mathrm{25}}} \\ $$$$\mathrm{c}\:−\:\sqrt{\mathrm{b}^{\mathrm{2}} \:−\:\frac{\mathrm{1}}{\mathrm{36}}}=\:\sqrt{\mathrm{a}^{\mathrm{2}} \:−\:\frac{\mathrm{1}}{\mathrm{36}}} \\ $$$$ \\ $$$$\mathrm{given}\:\mathrm{that}\:\mathrm{a},\:\mathrm{b},\:\mathrm{c}\:\mathrm{are}\:\mathrm{real}\:\mathrm{numbers}\: \\ $$$$\mathrm{that}\:\mathrm{satisfy}\:\mathrm{they}\:\mathrm{system}\:\mathrm{of}\:\mathrm{equation}\:... \\ $$$$\mathrm{if}\:\mathrm{a}\:+\:\mathrm{b}\:+\:\mathrm{c}\:=\:\frac{\mathrm{x}}{\sqrt{\mathrm{y}\:}}\:\mathrm{where}\:\mathrm{x},\:\mathrm{y}\:\mathrm{are}\: \\ $$$$\mathrm{positive}\:\mathrm{integers}\:\mathrm{and}\:\mathrm{y}\:\mathrm{is}\:\mathrm{square}\:\mathrm{free} \\ $$$$\mathrm{find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\mathrm{x}\:+\:\mathrm{y}\: \\ $$$$ \\ $$

Question Number 11813 Answers: 1 Comments: 3

Question Number 11805 Answers: 2 Comments: 0

x^y = y^x x^2 = y^3 find x and y

$$\mathrm{x}^{\mathrm{y}} \:=\:\mathrm{y}^{\mathrm{x}} \:\:\:\: \\ $$$$\mathrm{x}^{\mathrm{2}} \:=\:\mathrm{y}^{\mathrm{3}} \\ $$$$\mathrm{find}\:\mathrm{x}\:\mathrm{and}\:\mathrm{y} \\ $$

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