Question

Prove that (√2+1)(√2-1)=1.Use this to compute 1/√2+1 correct to two decimal places​

Answer 1

Given:- ( √2-1)(√2-1) = 1 . Also Calculate the value of 1/(√2+1) and 1/√2-1 .

To Prove:- LHS = RHS

Proof :- We have , (√2+1)(√2-1) = (√2)²-(1)² = 2-1 = 1

[ using the identity (a+b)(a-b)=a²-b² ]

→Now , 1/√2+1

= 1(√2-1)/(√2-1)(√2+1)

= √2-1 / 2-1

= √2 - 1 = 1.414 - 1 = 0.414 ≈ 0.41

→ 1/√2-1 = 1(√2+1)/(√2-1)(√2+1) = √2+1 / 2-1 = √2 + 1 = 1.414 + 1 = 2.414 ≈ 2.41

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