Question

prove that (2root+1) (2root-1) =1 using this calculate the value of 1/2root+1 and 1/2root-1
correct to two decimal places
​

Answer 1

Answer:

(6789+8907)

Step-by-step explanation:

455+78+:899"_7557

Answer 2

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

★ More to Know :-

• a² + b² = ( a + b )² - 2ab
• a² - b² = ( a + b )( a - b )
• ( a + b )² = a² + b² + 2ab.
• ( a - b )² = a² + b² - 2ab
• ( a + b )³ = a³ + b³ + 3ab(a + b)
• ( a - b )³ = a³ - b³ - 3ab ( a - b )
• a³ + b³ = ( a + b )( a² -ab + b²)
• a³ + b³ = ( a - b )( a² +ab + b²)