Question

VA ROG AJUTATIMA! SUNT NISTE SUBIECTE DE LA SIMULARE.. 1. se da: x=1/√2-1+1/√2+1
y=√2-(√2+1√2)
a) aratati: x * (√8-√2)=4
b)calculati: x²-y.

2. E(x)=x²+x+1)²-(x²+x)²-x² x∈R
Aratati ca E(n) este patrat perfect oricare ar fi numarul mic..

Answer 1

x=$\frac{1}{√2-1}$+$\frac{1}{√2+1}$⇒x=$\frac{√2+1}{2-1}$+$\frac{√2-1}{2-1}$⇒x=$\frac{√2+1+√2-1}{1}$⇒x=2√2
y=√2(√2+$\frac{1}{√2}$⇒y=√2×$\frac{2+1}{√2}$⇒y=3
a)x*(√8-√2)=4
2√2*(2√2-√2)=2√2*√2=2×2=4
b)x²-y
(2√2)²-3=4×2-3=8-3=5

5)E(x)=x⁴+x²+1+2x³+2x²+2x-x⁴-2x³-x²-x²
E(x)=x²+2x+1
E(x)=(x+1)²
E(n)=(n+1)²⇒E(n)-patrat perfect