Question

Find the value of a and b if 4+√2/2+√2=a-√b

Answer 1

$\sf given : - \: \frac{4 + \sqrt{2} }{2 + \sqrt{2} } = a - \sqrt{b} \\ \\ \sf here \: we \: have \: to \: find \: the \: value \: of \: \\ \sf a \: and \: b \\ \\ \sf so \: first \: we \: needa \: rationalize \: the \\ \sf denominator. \\ \\ \sf = \frac{4 + \sqrt{2} }{2 + \sqrt{2} } \times \frac{2 - \sqrt{2} }{2 - \sqrt{2} } \\ \\ \sf = \frac{(4 + \sqrt{2})(2 - \sqrt{2} ) }{(2 + \sqrt{2} )(2 - \sqrt{2} )} \\ \\ \sf = \frac{4(2 - \sqrt{2} ) + \sqrt{2} (2 - \sqrt{2} )}{( {2})^{2} - { (\sqrt{2} )}^{2} } \\ \\ \sf = \frac{8 - 4 \sqrt{2} + 2 \sqrt{2} - 2 }{4 - 2} \\ \\ \sf = \frac{ 6 - 2 \sqrt{2} }{2} \\ \\ \sf = \frac{( \cancel2 \times 3) - ( \cancel2 \times \sqrt{2}) }{ \cancel2} \\ \\ \sf = \boxed{3 - \sqrt{2} }$

comparing (3 - √2) with a - √b

➡ 3 - √2 = a - √b

hence, the value of a = 3 and b = 2

Answer 2

Answer:

4

Step-by-step explanation:

dvdhxgxggxhddhdj the answer is 67