Question

x=1/x-5 find x2-1/x2

Answer 1

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}