Question

Fara a rezolva ecuatia x^2-x-7=0 calculati(x1 si x2 fiind radacinile ecuatiei):
x1^4+x2^4

Answer 1

Răspuns:

Explicație pas cu pas

x1+x2=1

x1×x2=-7     cf Rel lui Viete

(x²+y²)²=x^4+y^4+2(xy)²

x²+y²=(x+y)²-2xy=S²-2P=1|+14=15

x*4+y*4=(x²+y²)²-2(xy)²=15²-2(-7)²=225-2×49=225-98=127

Answer 2

x²-x-7=0

x1+x2=1=> (x1+x2)²=1;

x1•x2=-7  => 2x1•x2=-14

x1²+x2²= (x1+x2)²-2•x1•x2=1+14=15

=>(x1²+x2²)²=15 ²=225

(x1)^4+(x2)^4=(x1²+x2²)²-2(x1•x2) ²

(x1)^4+(x2)^4=225-2(-7) ²=225-98

(x1)^4+(x2)^4=127