Question

if a=√2+1/√2-1 and b=√2-1/√2+1 then find the value of a2+b2-4ab

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Answer 1

Answer:

30

Step-by-step explanation:

$a = \frac{ \sqrt{2} + 1}{ \sqrt{2} - 1} = \frac{ (\sqrt{2} + 1 )}{( \sqrt{2} - 1) } \times \frac{( \sqrt{2} + 1) }{( \sqrt{2} + 1) } \\ \\ = \frac{2 + 1 + 2 \sqrt{2} }{2 - 1} \\ \\ = 3 + 2 \sqrt{2} \\ \\ b= \frac{ \sqrt{2} - 1}{ \sqrt{2} + 1} = \frac{ (\sqrt{2} - 1 )}{( \sqrt{2} + 1) } \times \frac{( \sqrt{2} - 1) }{( \sqrt{2} - 1) } \\ \\ = \frac{2 + 1 - 2 \sqrt{2} }{2 - 1} \\ \\ = 3 - 2 \sqrt{2} \\ \\ {a}^{2} + {b}^{2} - 4ab = 9 + 8 + 12 \sqrt{2} + 9 + 8 - 12 \sqrt{2} - 4(9 - 8)\\ \\ = 18 + 16 - 4\\ \\ = 34 - 4 = 30 \\ \\ = 30.$