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AlgebraQuestion and Answers: Page 5

Question Number 222141 Answers: 2 Comments: 0

x^2 +((x/(2x−1)))^2 =12

$${x}^{\mathrm{2}} +\left(\frac{{x}}{\mathrm{2}{x}−\mathrm{1}}\right)^{\mathrm{2}} =\mathrm{12} \\ $$

Question Number 222125 Answers: 4 Comments: 2

If: log_3 (5^x + (1/5^x ) + 7) ⇒ min = ?

$$\mathrm{If}:\:\:\:\mathrm{log}_{\mathrm{3}} \left(\mathrm{5}^{\boldsymbol{\mathrm{x}}} \:+\:\frac{\mathrm{1}}{\mathrm{5}^{\boldsymbol{\mathrm{x}}} }\:+\:\mathrm{7}\right)\:\:\:\Rightarrow\:\:\:\mathrm{min}\:=\:? \\ $$

Question Number 222076 Answers: 2 Comments: 0

Question Number 222066 Answers: 0 Comments: 4

Question Number 222031 Answers: 3 Comments: 0

x^x =−1 Number of solutions??

$${x}^{{x}} =−\mathrm{1} \\ $$$${Number}\:{of}\:{solutions}?? \\ $$

Question Number 222026 Answers: 2 Comments: 0

If (1.234)^a =(0.1234)^b =10^c prove that (1/a)−(1/c)=(1/b)

$${If}\:\left(\mathrm{1}.\mathrm{234}\right)^{{a}} =\left(\mathrm{0}.\mathrm{1234}\right)^{{b}} =\mathrm{10}^{{c}} \\ $$$${prove}\:{that}\:\frac{\mathrm{1}}{{a}}−\frac{\mathrm{1}}{{c}}=\frac{\mathrm{1}}{{b}} \\ $$

Question Number 222003 Answers: 2 Comments: 0

If a+b+c=0 then prove that (1/(x^b +x^(−c) +1))+(1/(x^c +x^(−a) +1))+(1/(x^a +x^(−b) +1))=1

$${If}\:{a}+{b}+{c}=\mathrm{0}\:{then}\:{prove}\:{that} \\ $$$$\frac{\mathrm{1}}{{x}^{{b}} +{x}^{−{c}} +\mathrm{1}}+\frac{\mathrm{1}}{{x}^{{c}} +{x}^{−{a}} +\mathrm{1}}+\frac{\mathrm{1}}{{x}^{{a}} +{x}^{−{b}} +\mathrm{1}}=\mathrm{1} \\ $$

Question Number 222001 Answers: 1 Comments: 6

(((4^(m+(1/4)) ×(√(2.2^m )))/(2.(√2^(−m) ))))^(1/m) =??

$$\left(\frac{\mathrm{4}^{{m}+\frac{\mathrm{1}}{\mathrm{4}}} ×\sqrt{\mathrm{2}.\mathrm{2}^{{m}} }}{\mathrm{2}.\sqrt{\mathrm{2}^{−{m}} }}\right)^{\frac{\mathrm{1}}{{m}}} =?? \\ $$

Question Number 221991 Answers: 1 Comments: 4

Simplify: 2^2 ∙ 2^(2^((70 − t_1 )/(10)) = ?)

$$\mathrm{Simplify}:\:\:\:\mathrm{2}^{\mathrm{2}} \:\centerdot\:\mathrm{2}^{\mathrm{2}^{\frac{\mathrm{70}\:−\:\boldsymbol{\mathrm{t}}_{\mathrm{1}} }{\mathrm{10}}} \:\:\:=\:\:\:?} \\ $$

Question Number 221968 Answers: 3 Comments: 0

(a+b+c)^3

$$\left({a}+{b}+{c}\right)^{\mathrm{3}} \\ $$

Question Number 221944 Answers: 1 Comments: 1

Question Number 221943 Answers: 1 Comments: 0

Question Number 221863 Answers: 1 Comments: 1

If a and b are whole numbers such a^b =121 then find the value of (a−1)^(b+1)

$${If}\:{a}\:{and}\:{b}\:{are}\:{whole}\:{numbers}\:{such}\:{a}^{{b}} =\mathrm{121} \\ $$$${then}\:{find}\:{the}\:{value}\:{of}\:\left({a}−\mathrm{1}\right)^{{b}+\mathrm{1}} \\ $$

Question Number 221856 Answers: 0 Comments: 3

Question Number 221848 Answers: 0 Comments: 2

Question Number 221829 Answers: 4 Comments: 0

(√(70.71.72.73+1))

$$\sqrt{\mathrm{70}.\mathrm{71}.\mathrm{72}.\mathrm{73}+\mathrm{1}} \\ $$

Question Number 221782 Answers: 0 Comments: 0

(((81))^(1/((27))^(1/3^a ) ) )^((√4)) where a=4^0^4^3 and b=Σ_(n=1) ^6 n

$$\left(\sqrt[{\sqrt[{\mathrm{3}^{{a}} }]{\mathrm{27}}}]{\mathrm{81}}\right)^{\sqrt{\mathrm{4}}} \\ $$$${where}\:{a}=\mathrm{4}^{\mathrm{0}^{\mathrm{4}^{\mathrm{3}} } } {and}\:{b}=\underset{{n}=\mathrm{1}} {\overset{\mathrm{6}} {\sum}}{n} \\ $$

Question Number 221778 Answers: 0 Comments: 0

For ∀n∈N^∗ ,n≥3 Prove: ∫_0 ^1 (Σ_(2<p≤2n) e^(2πip+α) )^2 e^(−4πinα) dα>0,p is a prime number

$$\mathrm{For}\:\forall{n}\in\boldsymbol{{N}}^{\ast} ,{n}\geq\mathrm{3}\:\mathrm{Prove}: \\ $$$$\int_{\mathrm{0}} ^{\mathrm{1}} \left(\underset{\mathrm{2}<{p}\leq\mathrm{2}{n}} {\sum}{e}^{\mathrm{2}\pi{ip}+\alpha} \right)^{\mathrm{2}} {e}^{−\mathrm{4}\pi{in}\alpha} {d}\alpha>\mathrm{0},{p}\:\mathrm{is}\:\mathrm{a}\:\mathrm{prime}\:\mathrm{number} \\ $$

Question Number 221754 Answers: 1 Comments: 0

((81))^(1/((64))^(1/((27))^(1/( 3^4^0^4^3 )) ) ) )^((√4))

$$\left.\sqrt[{\sqrt[{\sqrt[{\:\mathrm{3}^{\mathrm{4}^{\mathrm{0}^{\mathrm{4}^{\mathrm{3}} } } } }]{\mathrm{27}}}]{\mathrm{64}}}]{\mathrm{81}}\right)^{\sqrt{\mathrm{4}}} \\ $$

Question Number 221647 Answers: 0 Comments: 1

solve for x. x^1 + x^2 + x^3 = 4096

$${solve}\:{for}\:{x}. \\ $$$${x}^{\mathrm{1}} \:+\:{x}^{\mathrm{2}} \:+\:{x}^{\mathrm{3}} \:\:=\:\:\mathrm{4096} \\ $$

Question Number 221618 Answers: 3 Comments: 0

solve for x 2^x +4^x =8^x

$${solve}\:{for}\:{x} \\ $$$$\mathrm{2}^{{x}} +\mathrm{4}^{{x}} =\mathrm{8}^{{x}} \\ $$

Question Number 221669 Answers: 2 Comments: 3

Question Number 221585 Answers: 6 Comments: 1

solve for x ∈R (x^3 −6)^3 =x+6

$${solve}\:{for}\:{x}\:\in{R} \\ $$$$\left({x}^{\mathrm{3}} −\mathrm{6}\right)^{\mathrm{3}} ={x}+\mathrm{6} \\ $$

Question Number 221544 Answers: 1 Comments: 0

((x−1))^(1/(x+1)) = ((x+1))^(1/(x−1)) , x real

$$\:\:\sqrt[{{x}+\mathrm{1}}]{{x}−\mathrm{1}}\:=\:\sqrt[{{x}−\mathrm{1}}]{{x}+\mathrm{1}}\:,\:{x}\:{real}\: \\ $$

Question Number 221504 Answers: 1 Comments: 0

Find x if (x^4 /4^x )=(4^x /x^4 ) . x∈R

$${Find}\:{x}\:{if}\:\:\:\:\frac{{x}^{\mathrm{4}} }{\mathrm{4}^{{x}} }=\frac{\mathrm{4}^{{x}} }{{x}^{\mathrm{4}} }\:\:.\:\:\:{x}\in\mathbb{R} \\ $$

Question Number 221501 Answers: 3 Comments: 0

solve for x: (√(a−(√(a+x))))+(√(a+(√(a−x))))=2x it′s possible to solve for a but x seems impossible to me

$${solve}\:{for}\:\mathrm{x}: \\ $$$$\sqrt{\mathrm{a}−\sqrt{\mathrm{a}+\mathrm{x}}}+\sqrt{\mathrm{a}+\sqrt{\mathrm{a}−\mathrm{x}}}=\mathrm{2x} \\ $$$${it}'{s}\:{possible}\:{to}\:{solve}\:{for}\:\mathrm{a}\:{but}\:\mathrm{x}\:{seems} \\ $$$${impossible}\:{to}\:{me} \\ $$

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