Question

1)Daca x-1/x=3 ,x diferit 0 afla cat reperezinta x^2+1/x^2din300
2)Daca  a+b+c si ab+ac+bc=5,atunci a^2+b^2+c^2 este:

Answer 1

1)(x-1)/x=3

x-1=3x
x-3x=1
-2x=1
x= -1/2

(x-1)/x=3  |²

(x-1)²/x²=9

(x²-2x+1)/x²=9

(x²-2* (-1/2) +1)/x²=9

(x²+1+1)/x²=9

(x²+1)/x² -1/x²=9

(x²+1)/x² -1/(-1/2)=9

(x²+1)/x² -1/1 * ( -2/1)=9

(x²+1)/x² +2=9

(x²+1)/x²=9-2

(x²+1)/x²=7

p% din (x²+1)/x² = 300 <=> p/100 *7=300  <=> p/100=300/7

p=100*300/7= 30000/7= 4285,7%

2)a+b+c=4 |²

(a+b+c)²=16

a²+b²+c²+2ab+2ac+2bc=16

a²+b²+c²+2(ab+ac+bc)=16

a²+b²+c²+2*5=16

a²+b²+c²+10=16

a²+b²+c²=16-10

a²+b²+c²=6