Question

Aflați numerele raționale x care verifica egalitatiile:

Dau coroana

Answer 1

Răspuns:

Explicație pas cu pas:

a) [√(49·169)-7√81]/√576+24√(1521/64)=x·√49/[(2/3)²·√(729/100)]  ⇔

(7·13-7·9)/[24+24·(39/8)]=x·7/(2/3)²·(27/10)  ⇔

7(13-9)/(24+3·39)=x·7/(2·2·27/3·3·10)  ⇔7·4/(24+117)=x·7/(2·3/5)  ⇔

7·4/141=(x·7):6/5  ⇔4/141=x·5/6  ⇔5·x=24/141  ⇔5·x=8/47  ⇒x=(8/47):5  ⇔

x=8/(47·5)  ⇔x=8/235

b) x/[√(900/49)-√(784/225) ·15/7]=(√676-√576)/0,(5)·√(1296/625)  ⇔

x/[30/7-(28/15)·15/7]=(26-24)/[(5/9)·(36/25)]  ⇔

x/(30/7-4)=2/(5·36/9·25)  ⇔x/(30-28)/7=2/(4/5)  ⇔x/(2/7)=2/(4/5)  ⇔

7·x/2=2·5/4  ⇔7·x/2=5/2  ⇔7·x=2·5/2  ⇔7·x=5  ⇔x=5/7