Question

3-2×√2=a+b×√2then b =​

Answer 1

Answer:

$3-2\sqrt{2}=a+b\sqrt{2}\quad :\quad b=\dfrac{3\sqrt{2}-4-\sqrt{2}a}{2}$

Step-by-step explanation:

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$3-2\sqrt{2}=a+b\sqrt{2}$

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$\mathrm{Switch\:sides}$

$a+b\sqrt{2}=3-2\sqrt{2}$

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$\mathrm{Subtract\:}a\mathrm{\:from\:both\:sides}$

$a+b\sqrt{2}-a=3-2\sqrt{2}-a$

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$\mathrm{Simplify}$

$b\sqrt{2}=3-2\sqrt{2}-a$

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$\mathrm{Divide\:both\:sides\:by\:}\sqrt{2}$

$\dfrac{b\sqrt{2}}{\sqrt{2}}=\dfrac{3}{\sqrt{2}}-\dfrac{2\sqrt{2}}{\sqrt{2}}-\dfrac{a}{\sqrt{2}}$

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$\mathrm{Simplify}$

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$\mathrm{Simplify\:}\dfrac{b\sqrt{2}}{\sqrt{2}}:\quad b$

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$\mathrm{Simplify\:}\dfrac{3}{\sqrt{2}}-\dfrac{2\sqrt{2}}{\sqrt{2}}-\dfrac{a}{\sqrt{2}}$

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$\dfrac{3}{\sqrt{2}}-\dfrac{2\sqrt{2}}{\sqrt{2}}-\dfrac{a}{\sqrt{2}}$

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$\mathrm{Apply\:rule}\:\dfrac{a}{c}\pm \dfrac{b}{c}=\dfrac{a\pm \:b}{c}$

$=\dfrac{3-2\sqrt{2}-a}{\sqrt{2}}$

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$\mathrm{Multiply\:by\:the\:conjugate}\:\dfrac{\sqrt{2}}{\sqrt{2}}$

$=\dfrac{\left(3-2\sqrt{2}-a\right)\sqrt{2}}{\sqrt{2}\sqrt{2}}$

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$\mathrm{Simplify}$

$=\dfrac{3\sqrt{2}-4-\sqrt{2}a}{2}$

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$b=\dfrac{3\sqrt{2}-4-\sqrt{2}a}{2}$