Math, asked by sahashweta80, 2 months ago

If ( x - 1/x ) = 3 , then find the value of ( x + 1/x )^2
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Answers

Answered by testingpurpose152001
12

Answer:

The answer to this question is 13

Step-by-step explanation:

Given that,

           x -\frac{1}{x} = 3

Now,

(x+\frac{1}{x})^2 = x^2 +\frac{1}{x^2} +2\cdot x\cdot \frac{1}{x}\\=x^2 +\frac{1}{x^2} +2\\=(x-\frac{1}{x})^2 + 4\\=9+4 = 13

Answered by amansharma264
5

EXPLANATION.

⇒ (x - 1/x) = 3.

As we know that,

Squaring on both sides of the equation, we get.

⇒ (x - 1/x)² = (3)².

⇒ (x)² + (1/x)² - 2(x)(1/x) = 9.

⇒ x² + 1/x² - 2 = 9.

⇒ x² + 1/x² = 9 + 2.

⇒ x² + 1/x² = 11.

As we know that,

Formula of :

⇒ (a + b)² = a² + b² + 2ab.

⇒ (x + 1/x)² = x² + 1/x² + 2(x)(1/x).

Put the values of (x² + 1/x²) = 11 in the equation, we get.

⇒ (x + 1/x)² = x² + 1/x² + 2.

⇒ (x + 1/x)² = 11 + 2.

(x + 1/x)² = 13.

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