Question

If p(x)=x² - 2√2 + 1, then find value of p(2√2).

Answer 1

p(x)=x² - 2√2 + 1

p(2√2)=(2√2)² - 2√2 + 1

= (2√2)² - 2.2√2.(1/2) + (1/2)²

- (1/2)² + 1

=(2√2 - 1/2)² - 3/4

=(2√2 - 1/2)² - (√3/2)²

=(2√2-1/2+√3/2)(2√2-1/2-√3/2)