Question

if 4+√2÷2+√2=a-√b find the value of a and b​

Answer 1

Answer:

$4 + \sqrt{2} \div 2 + \sqrt{2} = a - \sqrt{b} \\ \implies \: 4 + \frac{ \sqrt{2} }{2} + \sqrt{2} = a - \sqrt{b} \\ \implies \: 4 + \frac{1 }{ \sqrt{2} } + \sqrt{2} = a - \sqrt{b} \\ \implies \: 4 + \frac{1 + \sqrt{2} \times \sqrt{2} }{ \sqrt{2} } = a - \sqrt{b} \\ \implies \: 4 + \frac{1 + 2 }{ \sqrt{2} } = a - \sqrt{b} \\ \implies \: 4 + \frac{3}{ \sqrt{2} } = a - \sqrt{b} \\ \implies \: 4 + \frac{3 \times \sqrt{2} }{ \sqrt{2} \times \sqrt{2} } = a - \sqrt{b} \\ \implies \: 4 + \frac{3 \sqrt{2} }{2 } = a - \sqrt{b} \\ equatig \: like \: terms \: from \: both \: \\ sides \\ \implies \huge \fbox{a = 4} \\ \implies \frac{3 \sqrt{2} }{2 } = - \sqrt{b} \\ \implies \: (\frac{3 \sqrt{2} }{2 })^{2} = ( - \sqrt{b} )^{2} \\ \implies \: \frac{9 \times 2 }{4 } ={b} \\ \implies \: \frac{9 }{2} ={b} \\ \implies \huge \fbox{b \: = \frac{9}{2} }$

Answer 2

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