Question

The number of solutions of (x 2 + 1) 2 + 2(x 2 + 1) - 3 = 0 is equal to

A. 1
B. 2
C. 3
D. 4

Need a correct explanation from everyone !!​

Answer 1

2

Explanation:

simplify the equation to

`2{x}^(2) + 2 + 2 {x}^(2) + 2 - 3 = 0`

simplify again by combining lIke terms to get

`4 {x}^(2) + 1 = 0`

since x 2 can mean that x can be both a positive and negative number so there can be 2 solutions. they will both involve imaginary numbers because 4x 2 is guaranteed to be positive

Answer 2

To determine the number of solutions of the given equation, let's simplify it first:

(x^2 + 1)^2 + 2(x^2 + 1) - 3 = 0

Let's substitute a new variable, let's say u = x^2 + 1, to simplify the equation further:

u^2 + 2u - 3 = 0

Now, we have a quadratic equation in terms of u. To find the solutions for u, we can factorize the equation:

(u + 3)(u - 1) = 0

This equation will be true if either (u + 3) equals zero or (u - 1) equals zero.

For (u + 3) = 0, we have u = -3.

For (u - 1) = 0, we have u = 1.

Now, let's substitute back u = x^2 + 1:

For u = -3:

x^2 + 1 = -3

x^2 = -4

This equation has no real solutions because the square of any real number cannot be negative.

For u = 1:

x^2 + 1 = 1

x^2 = 0

This equation has a single solution: x = 0.

Therefore, the given equation has only one solution, x = 0.

The correct answer is A. 1.

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