Let a and b be positive real numbers such that

a^2 + b^2 = 1

Prove that

a^4 + b^4 is greater than or equal to 0.5

Would someone be so kind as to point me in the right direction?

P.S. Don't give me the answer just yet. I want to see if I can do it alone. Just give me an idea of how I should go about doing this.