Question

Find the value of a and b, if
√2+1 /√2-1 - √2-1/√2+1 = a+√23​

Answer 1

Answer:

a = √2

Step-by-step explanation:

According to the question,

     $\frac{\sqrt{2}+1 }{\sqrt{2}-1 } - \frac{\sqrt{2} -1}{\sqrt{2} +1} = a + 3\sqrt{2}$

=> $\frac{(\sqrt{2} +1)^{2} -(\sqrt{2} -1)^{2} }{(\sqrt{2} -1)*(\sqrt{2} +1)} = a+3\sqrt{2}$

=> $\frac{4*\sqrt{2} *1}{\sqrt{2} ^{2}-1^{2} }$ = a + 3√2     [∵ 4ab = (a + b)² - (a - b)²; a² - b² = (a + b) × (a - b)]

=> 4√2 = a + 3√2

=> a = √2