Question

2. Se consideră expresia E(x) = (x+√√2)² + (1-x√√2)² + x(3-x)-2, unde x este a) Arată că E(x) = (x + 1)(2x + 1), pentru orice număr real x. dele de teste​

Answer 1

$E(x)=\Big(x+\sqrt{2} \Big)^2+\Big(1-x\sqrt{2} \Big)+x(3-x)-2\\\\ E(x)=x^2+2 \cdot x \cdot \sqrt{2} +\Big(\sqrt{2} \Big)^2+1^2 -2\cdot1\cdot x\sqrt{2} +\Big(x\sqrt{2} \Big)^2+3x-x^2-2\\\\ E(x)=x^2+2x\sqrt{2} +2+1-2x\sqrt{2} +2x^2+3x-x^2-2\\\\ E(x)=2x^2+3x+1\\\\ E(x)=2x^2+2x+x+1\\\\ E(x)=2x(x+1)+1(x+1)\\\\ E(x)=(x+1)(2x+1)$