Question

find the range of y=x^2+1/x^2-1​

Answer 1

Answer:

y ≤ - 1 ,  y > 1  or  (-∞ , -1] ∪ (1 , ∞)

Step-by-step explanation:

⇒ y(x² - 1) = x² + 1

⇒ yx² - y = x² + 1

⇒ yx² - y - x² - 1 = 0

⇒ x²(y - 1) - (y + 1) = 0

⇒ x²(y - 1) - 0x - (y + 1) = 0

    For the value of x to be real, discriminant must be 0 or greater than 0.

⇒ discriminant ≥ 0

⇒ (0)² - 4[-(y - 1)(y + 1)] ≥ 0

⇒ 4(y - 1)(y + 1) ≥ 0

⇒ 4(y - 1)(y + 1) ≥ 0

   y ≤ - 1 ,  y > 1    [as for y=1, it will be false]