Question

Determinati x apartine nr.reale astfel incat 34+15(x+3)²=(-13)²

Answer 1

34+15(x+3)²=(-13)²
34+15(x²+6x+9)=169
34+15x²+90x+135=169
15x²+90x+169=169
15x²+90x+169-169=0
15x²+90x+0=0

Δ=b²-4ac=90²-4×15×0=8100

x1=(-b+√Δ)2a=(-90+√8100)/2×15=0
x2=(-b-√Δ)/2a=(-90-√8100)/2×15=(-90-90)/30=-180/30=-6

verificare . in loc de x vom scrie -6

34+15((-6)+3)²=34+15×(-3)²=34+15×9=34+135=169
169=(-13)²

deci x=-6, iar {-6}∈R