If 4x + y = 1 and 4x - y = 4, then the values of x and y respectively are-

If 4^{x + y} = 1 and 4^{x - y} = 4, then the values of x and y respectively are-

A - 1/2 and 1/2

B - 1/2 and - 1/2

C 1/2 and - 1/2

D 1/2 and 1/2

Solution

Correct Answer: Option C

4^{x + y} = 1
⇒ 4^{x + y} = 4⁰
⇒ x + y = 0

4^{x - y} = 4
⇒4^{x - y} = 4¹
⇒ x - y = 1

x + y + x - y = 1
⇒ 2x = 1
∴ x = 1/2

1/2 - y = 1
⇒ y = (1/2) - 1
⇒ y = (1 - 2)/2
∴ y = - 1/2

Solution

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