If x⁴ - y⁴ = -15 and x² - y² = -3, what is the value of x² + y² ?

The correct answer is: 5

HINT: Use the appropriate algebraic identity and solve.
Complete step by step solution:
Let x⁴ - y⁴ = -15…(i) and x² -y² = -3…(ii)
We know the algebraic identity a² - b² = (a + b) (a - b)
Here in (i), it can be written as (x²)² - (y²)² = -15…(iii)
According to the identity, we can write (iii) as (x² + y²) (x² - y²) = -15…(iv)
From (ii), we know that x² - y² = -3
On substituting this in (iv), we get (x² + y²)(-3) = -15
On dividing both the sides by -3, we get (x² + y²) = 5
So, (x² + y²) = 5
Hence option A is the correct answer.
Note: Till (iv) it is the same as the above method. Then we know that x² - y² = -3, On substitution, we get
(x² + y²)(-3) = -15, Next we can compare each option value with the given equation until we get the value of
(x² + y²). We get it to be 5 and hence option A becomes the answer.