Question

if x2+1/x2=3 find the value of x+1/x

Answer 1

✏ using the identity :

$(x + \frac{1}{x} ) {}^{2} = x {}^{2} + \frac{1}{x {}^{2} } + 2(x)( \frac{1}{x} ) \\ (x + \frac{1}{x} ) {}^{2} = 3 + 2 \\ (x + \frac{1}{x} ) {}^{2} = 5 \\ x + \frac{1}{x} = \sqrt{5}$

Hope it helps

Answer 2

Step-by-step explanation:

Given--->

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x² + 1/x² = 3

To fund---> x + 1 / x = ?

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Solution--->

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We have an identity

(a + b )² = a² + b² + 2ab

Now

(x + 1/x)² = x² + 1/ x² + 2 x (1/x)

= x² + 1/x² + 2

=(x² + 1/x²) + 2

=(3) + 2

(x + 1/x)² = 5

Taking square root of both sides

x + 1/x = √5

Additional information--->

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1) (a - b)² =a² + b² - 2ab

2) (a + b )³ = a³ + b³ +3ab (a + b )

3) (a - b )³ = a³ - b³ - 3 a b (a - b )

4)(a + b + c)² = a²+b²+c²+2ab+2ac+2bc

5) a³ + b³ = (a + b) (a² + b² -ab)

6)a³ - b³ = (a - b) (a² + b² + ab)