Question

x^2-1/x+1=3 find the x​

Answer 1

Answer:

x=4

Step-by-step explanation:

x²-1 /x+1 = 3

x²-1 = 3(x+1)

x² = 3x + 3 + 1

x² - 3x - 4 = 0

by quadratic equation,

x-4=0 (or) x+1=0

x=4 x= -1(since (-) can't be taken)

therefore, X = 4

I think this is the answer

Answer 2

Solution!!

x² - (1/x) + 1 = 3

Move the constant to the left-hand side and change its sign.

x² - (1/x) + 1 - 3 = 0

Calculate the difference.

x² - (1/x) - 2 = 0

Write all the numerators above the common denominator.

(x³ - 1 - 2x)/x = 0

When the quotient of expressions equals 0, the numerator has to be 0.

x³ - 1 - 2x = 0

x³ - 2x - 1 = 0

Add and subtract x².

x³ + x² - x² - 2x - 1 = 0

Write -2 as a difference.

x³ + x² - x² - x - x - 1 = 0

Make the factors.

x²(x + 1) - x(x + 1) - (x + 1) = 0

(x + 1)(x² - x - 1) = 0

When the product of factors equals 0, atleast one factor is 0.

x + 1 = 0

x² - x - 1 = 0

x = -1

x² - x - 1 = 0

Using the quadratic formula.

x = -1

x = -1x = (1 + √5)/2

x = -1x = (1 + √5)/2x = (1 - √5)/2

Hence we have three solutions for the equation.