Question

If x = 1/x-5, find x2- 1/x2
urgent

Answer 1

Answer:

Step-by-step explanation:

Answer 2

Answer:

Value of $x^2-\frac{1}{x^2}\:is\:-5\sqrt{29}$

Step-by-step explanation:

Given: $x=\frac{1}{x}-5\:\:\implies\:\:x-\frac{1}{x}=-5$

To find: $x^2-\frac{1}{x^2}$

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

put a = x and b = 1/x

$(x+\frac{1}{x})^2=(x-\frac{1}{x})^2+4\times x\times\frac{1}{x}$

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

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

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

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

put a = x and y = 1/x

we get,

$x^2-(\frac{1}{x})^2=(x+\frac{1}{x})(x-\frac{1}{x})$

$x^2-\frac{1}{x^2}=(\sqrt{29})(-5)$

$x^2-\frac{1}{x^2}=-5\sqrt{29}$

Therefore, Value of $x^2-\frac{1}{x^2}\:is\:-5\sqrt{29}$