Question

Number of values of a for which for the system

2^|x| + |x| = y + x²+ a and x² + y² = 1 has only one solution where a ,x ,y are real is

• A. 1
• B. 2
• C. Finite but more than two
• D. Infinite

Answer 1

Answer: (A)

1

Answer 2

Let (x₁, y₁) is solution

from both equation x is symmetric

So (–x₁, y₁) is also solution

but unique solution ̃ x₁ = – x₁ ̃ x₁ = 0

So y₁ = ± 1 ̃ y₁ = 1 ̃ a = 0 ̃ (0, 1)

y₁ = – 1 ̃ a = 2

for a = 0 2^|x| + |x| = y + x² ̃ (0, 1) only on solution.

for a = 2 2^|x| + |x| = y + x² + 2 ̃ (0, 1)

& (2, 0), (–2, 0) & (1, 0), (–1, 0)

Hence a = 0 is acceptable