Question

Find the value of x2 + 1/x2, if x – 1/x = root 3

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Answer 1

Step-by-step explanation:

Given -

x - 1/x = √3

To Find :-

Value of x² + 1/x²

As Given :-

x - 1/x = √3

Now,

Squaring both sides :-

» (x - 1/x)² = (√3)²

» x² + 1/x² - 2× x × 1/x = 3

» x² + 1/x² - 2 = 3

» x² + 1/x² = 3 + 2

» x² + 1/x² = 5

Hence,

The value of x² + 1/x² is 5

Formula Used :-

• (a - b)² = a² - 2ab + b²

Some related formulas :-

• (a + b)² = a² + 2ab + b²
• (a + b)(a - b) = a² - b²
• (a + b)³ = a³ + 3a²b + 3b²a + b³
• (a - b)³ = a³ - 3a²b + 3b²a - b³

Answer 2

x2 + 1/x2=a

(x2-1)/x=√3

3=((x2-1)2)/x2

a=(x4+1)/x2

3=(x4+1+2×x2)/x2

=>3=a+2. ((x4+1)/x2)+((2×x2)/x2)

=>1=a