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AlgebraQuestion and Answers: Page 310

Question Number 62276 Answers: 1 Comments: 0

{ ((((√x)/a)+((√y)/b)=1)),((((√a)/x)+((√b)/y)=1)) :} a,b∈R^+

$$\begin{cases}{\frac{\sqrt{\boldsymbol{\mathrm{x}}}}{\boldsymbol{\mathrm{a}}}+\frac{\sqrt{\boldsymbol{\mathrm{y}}}}{\boldsymbol{\mathrm{b}}}=\mathrm{1}}\\{\frac{\sqrt{\boldsymbol{\mathrm{a}}}}{\boldsymbol{\mathrm{x}}}+\frac{\sqrt{\boldsymbol{\mathrm{b}}}}{\boldsymbol{\mathrm{y}}}=\mathrm{1}}\end{cases}\:\:\:\boldsymbol{\mathrm{a}},\boldsymbol{\mathrm{b}}\in\mathrm{R}^{+} \\ $$

Question Number 62275 Answers: 1 Comments: 0

{ ((a(√x)+b(√y)=2(√(ab)))),((x(√a)+y(√b)=2(√(ab)))) :} a,b∈R^+

$$\begin{cases}{\boldsymbol{\mathrm{a}}\sqrt{\boldsymbol{\mathrm{x}}}+\boldsymbol{\mathrm{b}}\sqrt{\boldsymbol{\mathrm{y}}}=\mathrm{2}\sqrt{\boldsymbol{\mathrm{ab}}}}\\{\boldsymbol{\mathrm{x}}\sqrt{\boldsymbol{\mathrm{a}}}+\boldsymbol{\mathrm{y}}\sqrt{\boldsymbol{\mathrm{b}}}=\mathrm{2}\sqrt{\boldsymbol{\mathrm{ab}}}}\end{cases}\:\:\:\:\:\:\boldsymbol{\mathrm{a}},\boldsymbol{\mathrm{b}}\in\mathrm{R}^{+} \\ $$

Question Number 62234 Answers: 1 Comments: 0

Question Number 62228 Answers: 0 Comments: 2

{ (((√(a+x))+(√(a−y))=2a)),(((√(a−x))+(√(a+y))=2a)) :} a∈R.

$$\begin{cases}{\sqrt{\boldsymbol{\mathrm{a}}+\boldsymbol{\mathrm{x}}}+\sqrt{\boldsymbol{\mathrm{a}}−\boldsymbol{\mathrm{y}}}=\mathrm{2}\boldsymbol{\mathrm{a}}}\\{\sqrt{\boldsymbol{\mathrm{a}}−\boldsymbol{\mathrm{x}}}+\sqrt{\boldsymbol{\mathrm{a}}+\boldsymbol{\mathrm{y}}}=\mathrm{2}\boldsymbol{\mathrm{a}}}\end{cases}\:\:\:\:\:\boldsymbol{\mathrm{a}}\in\boldsymbol{\mathrm{R}}. \\ $$

Question Number 62211 Answers: 0 Comments: 3

(x/((√(4−x^2 ))+3))Max=(5/3)?

$$\frac{{x}}{\sqrt{\mathrm{4}−{x}^{\mathrm{2}} }+\mathrm{3}}{Max}=\frac{\mathrm{5}}{\mathrm{3}}? \\ $$

Question Number 62184 Answers: 0 Comments: 1

((2x−1))^(1/3) + (√(3x+1)) = 3(x)^(1/4)

$$\sqrt[{\mathrm{3}}]{\mathrm{2}{x}−\mathrm{1}}\:+\:\sqrt{\mathrm{3}{x}+\mathrm{1}}\:=\:\mathrm{3}\sqrt[{\mathrm{4}}]{{x}} \\ $$

Question Number 62176 Answers: 2 Comments: 0

Question Number 62169 Answers: 1 Comments: 0

Prove without induction that: (1 + (√2))^(2n) + (1 − (√2))^(2n) is even for every natural number n.

$$\mathrm{Prove}\:\mathrm{without}\:\mathrm{induction}\:\mathrm{that}:\:\:\left(\mathrm{1}\:+\:\sqrt{\mathrm{2}}\right)^{\mathrm{2n}} \:+\:\left(\mathrm{1}\:−\:\sqrt{\mathrm{2}}\right)^{\mathrm{2n}} \:\:\mathrm{is}\:\mathrm{even}\:\mathrm{for}\:\mathrm{every} \\ $$$$\mathrm{natural}\:\mathrm{number}\:\mathrm{n}.\:\:\: \\ $$

Question Number 62142 Answers: 0 Comments: 0

6.38÷0.2

$$\mathrm{6}.\mathrm{38}\boldsymbol{\div}\mathrm{0}.\mathrm{2} \\ $$

Question Number 62140 Answers: 1 Comments: 0

2÷(1/3)

$$\mathrm{2}\boldsymbol{\div}\frac{\mathrm{1}}{\mathrm{3}} \\ $$

Question Number 62138 Answers: 0 Comments: 0

5^1

$$\mathrm{5}^{\mathrm{1}} \\ $$

Question Number 62137 Answers: 0 Comments: 0

((1/4))^3

$$\left(\frac{\mathrm{1}}{\mathrm{4}}\right)^{\mathrm{3}} \\ $$

Question Number 62136 Answers: 0 Comments: 0

3 of (1/6)

$$\mathrm{3}\:\mathrm{of}\:\frac{\mathrm{1}}{\mathrm{6}} \\ $$

Question Number 62135 Answers: 0 Comments: 0

(√(100))

$$\sqrt{\mathrm{100}} \\ $$

Question Number 62134 Answers: 0 Comments: 0

8^4 ×8^2

$$\mathrm{8}^{\mathrm{4}} ×\mathrm{8}^{\mathrm{2}} \\ $$

Question Number 62133 Answers: 0 Comments: 0

5(2+3+1)

$$\mathrm{5}\left(\mathrm{2}+\mathrm{3}+\mathrm{1}\right) \\ $$

Question Number 62132 Answers: 0 Comments: 0

(3×2)^2

$$\left(\mathrm{3}×\mathrm{2}\right)^{\mathrm{2}} \\ $$

Question Number 62131 Answers: 0 Comments: 0

(1/3)+3(1/4)

$$\frac{\mathrm{1}}{\mathrm{3}}+\mathrm{3}\frac{\mathrm{1}}{\mathrm{4}} \\ $$

Question Number 62112 Answers: 2 Comments: 0

Question Number 62092 Answers: 0 Comments: 1

MATH MEME: 3+x = 1+8 :) ((3+x)/+) = ((1+8)/+) cancel the plus sign 3x = 18 ((3x)/3) = ((18)/3) x = 6 am i correct?

$$\mathrm{MATH}\:\mathrm{MEME}: \\ $$$$\mathrm{3}+\mathrm{x}\:=\:\mathrm{1}+\mathrm{8} \\ $$$$\left.:\right) \\ $$$$\frac{\mathrm{3}+\mathrm{x}}{+}\:=\:\frac{\mathrm{1}+\mathrm{8}}{+} \\ $$$${cancel}\:{the}\:{plus}\:{sign} \\ $$$$\mathrm{3}{x}\:=\:\mathrm{18} \\ $$$$\frac{\mathrm{3}{x}}{\mathrm{3}}\:=\:\frac{\mathrm{18}}{\mathrm{3}} \\ $$$$\boldsymbol{{x}}\:=\:\mathrm{6} \\ $$$$\boldsymbol{{am}}\:\boldsymbol{{i}}\:\boldsymbol{{correct}}? \\ $$

Question Number 62057 Answers: 1 Comments: 2

2^(−2)

$$\mathrm{2}^{−\mathrm{2}} \\ $$

Question Number 62055 Answers: 0 Comments: 0

$8+$3

$$\$\mathrm{8}+\$\mathrm{3} \\ $$

Question Number 62054 Answers: 0 Comments: 1

484×27

$$\mathrm{484}×\mathrm{27} \\ $$

Question Number 62053 Answers: 0 Comments: 1

m5=25

$$\mathrm{m5}=\mathrm{25} \\ $$

Question Number 62052 Answers: 0 Comments: 1

3(1/4)−(3/4)

$$\mathrm{3}\frac{\mathrm{1}}{\mathrm{4}}−\frac{\mathrm{3}}{\mathrm{4}} \\ $$

Question Number 62051 Answers: 0 Comments: 1

(7^5 /7^3 )

$$\frac{\mathrm{7}^{\mathrm{5}} }{\mathrm{7}^{\mathrm{3}} } \\ $$

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