Question

if X = 1/ √2+1 then the value of X2 +2x-1is​

Answer 1

Answer :

x² + 2x - 1 = 0

Solution :

• Given : x = 1/(√2 + 1)
• To find : x² + 2x - 1 = ?

We have ;

x = 1/(√2 + 1)

Now ,

Rationalising the denominator of the term in RHS , we have ;

=> x = (√2 - 1) / (√2 + 1)(√2 - 1)

=> x = (√2 - 1) / [ (√2)² - 1² ]

=> x = (√2 - 1) / (2 - 1)

=> x = √2 - 1

=> x + 1 = √2

Now ,

Squaring both the sides , we have ;

=> (x + 1)² = (√2)²

=> x² + 2•x•1 + 1² = 2

=> x² + 2x + 1 = 2

=> x² + 2x + 1 - 2 = 0

=> x² + 2x - 1 = 0

Hence , x² + 2x - 1 = 0 .