Question

If x² +1/x²=7 then x - 1/x is equal to
a) 4
b) +5
c) 0
d) +7​

Answer 1

Answer :

x - 1/x = √5

Note :

• (a + b)² = a² + b² + 2ab

• (a - b)² = a² + b² - 2ab

• (a + b)(a - b) = a² - b²

• (a + b)³ = a³ + b³ + 3ab(a + b)

• (a - b)³ = a³ + b³ - 3ab(a - b)

• a³ + b³ = (a + b)(a² + b² - ab)

• a³ - b³ = (a - b)(a² + b² + ab)

• (a + b)² = (a - b)² + 4ab

• (a - b)² = (a + b)² - 4ab

Solution :

• Given : x² + 1/x² = 7
• To find : x - 1/x = ?

We have ;

x² + 1/x² = 7

Also ,

We know that , (a - b)² = a² + b² - 2ab

Taking a = x and b = 1/x in the above identiry , We get ;

=> (x - 1/x)² = x² + 1/x² - 2•x•(1/x)

=> (x - 1/x)² = 7 - 2

=> (x - 1/x)² = 5

=> x - 1/x = √5

Hence,

x - 1/x = √5