Question

if x+1/x = X2+1/x2 with step by step ​

Answer 1

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Answer 2

Answer:

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Value of x^2-\frac{1}{x^2}\:is\:-5\sqrt{29}x2−x21is−529

Step-by-step explanation:

Given: x=\frac{1}{x}-5\:\:\implies\:\:x-\frac{1}{x}=-5x=x1−5⟹x−x1=−5

To find: x^2-\frac{1}{x^2}x2−x21

We know that (a + b)² = (a - b)² + 4ab

put a = x and b = 1/x

(x+\frac{1}{x})^2=(x-\frac{1}{x})^2+4\times x\times\frac{1}{x}(x+x1)2=(x−x1)2+4×x×x1

(x+\frac{1}{x})^2=(-5)^2+4(x+x1)2=(−5)2+4

(x+\frac{1}{x})^2=25+4(x+x1)2=25+4

x+\frac{1}{x}=\sqrt{29}x+x1=29

Now, we know that a² - b² = (a + b)(a -b)

put a = x and y = 1/x

we get,

x^2-(\frac{1}{x})^2=(x+\frac{1}{x})(x-\frac{1}{x})x2−(x1)2=(x+x1)(x−x1)

x^2-\frac{1}{x^2}=(\sqrt{29})(-5)x2−x21=(29)(−5)

x^2-\frac{1}{x^2}=-5\sqrt{29}x2−x21=−529

Therefore, Value of x^2-\frac{1}{x^2}\:is\:-5\sqrt{29}x2−x21is−529