Question

Find a and b if 4+root2 by 2 +root2 =a-root b

Answer 1

$\textbf{Given:}$

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

$\textbf{To find:}$

$\text{The values of a and b}$

$\textbf{Solution:}$

$\text{Consider,}$

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

$\text{To rationalize the denominator multiply both numerator}$

$\text{denominator by 2-\sqrt{2} }$

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

$\dfrac{(4+\sqrt{2})(2-\sqrt{2})}{(2+\sqrt{2})(2-\sqrt{2})}=a-\sqrt{b}$

$\dfrac{8-4\sqrt{2}+2\sqrt{2}-2}{4-2}=a-\sqrt{b}$

$\dfrac{6-2\sqrt{2}}{2}=a-\sqrt{b}$

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

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

$\text{Comparing on bothsides, we get}$

$a=3\;\text{and}\;b=2$

$\therefore\textbf{The value of a and b are 3 and 2}$

Find more:

√7 - 2/√7 + 2 = a√7 + b

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If x = √7+ √3 and xy = 4, then x4 + y4 =​

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Answer 2

The answer is in the attachment

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