Question

Va roog dau coroana ​

Answer 1

Răspuns:

x+1/x=6

Ridici ambii  membrii  la  patrat

(x+1/x)²=6²

x²+2*x*1/x+1/x²=36

x²+2+1/x²=36

x²+1/x²=36-2

x²+1/x²=34

---------------------------------

x+1/x=6

x²+1=6x

x²-6x+1=0

Δ=36-4=32

√Δ=√32=4√2

x1=(6-4√2)/2=3-2√2

x2=(6+4√2)/2=3+2√2

Observi ca  x1*x2=(3-2√2)*(3+2√2)=9-8=1

x1*x2=1=> x1=1/x2=>

x-1/x=3-2√2-1/(3+2√2)=[(3-2√2)*(3+2√2)-1]/(3+2√2)=(9-8-1)/(3+2√2)=0

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