Question

using identity (a+b)^2 = a^2 + 2ab + b^2 find the value of x^2 + 1/x^2 if x+1/x = 3​

Answer 1

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Answer 2

Answer:

x² + 1/x² = 7

Note:

★ (a + b)² = a² + 2ab + b²

★ (a - b)² = a² - 2ab + b²

★ a² - b² = (a + b)(a - b)

★ (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)

Solution:

Given : x + 1/x = 3

To find : x² + 1/x² = ?

We have ;

x + 1/x = 3

Now,

Squaring both sides , we get ;

=> (x + 1/x)² = 3²

=> x² + 2•x•(1/x) + (1/x)² = 9

=> x² + 2 + 1/x² = 9

=> x² + 1/x² = 9 - 2

=> x² + 1/x² = 7

Hence,

The required answer is 7 .