if x=7+4√3, find √x+(1/√x)
Answers
Given that,
So,
can be further rewritten as
Now, Consider,
On rationalizing the denominator, we get
So,
Thus, On adding equation (1) and (2), we get
Hence,
More Identities to know:
(a + b)² = a² + 2ab + b²
(a - b)² = a² - 2ab + b²
a² - b² = (a + b)(a - b)
(a + b)² = (a - b)² + 4ab
(a - b)² = (a + b)² - 4ab
(a + b)² + (a - b)² = 2(a² + b²)
(a + b)³ = a³ + b³ + 3ab(a + b)
(a - b)³ = a³ - b³ - 3ab(a - b)
Answer:
Given that,
So,
can be further rewritten as
Now, Consider,
On rationalizing the denominator, we get
So,
Thus, On adding equation (1) and (2), we get
Hence,
More Identities to know:
(a + b)² = a² + 2ab + b²
(a - b)² = a² - 2ab + b²
a² - b² = (a + b)(a - b)
(a + b)² = (a - b)² + 4ab
(a - b)² = (a + b)² - 4ab
(a + b)² + (a - b)² = 2(a² + b²)
(a + b)³ = a³ + b³ + 3ab(a + b)
(a - b)³ = a³ - b³ - 3ab(a - b)