REZOLVARE TESTUL 4
1) log2( 8) +(1/2) ^- 1 - ∛125 = 0
log2( 2³) + 2 - ∛5³ = 0
3 + 2 - 5 = 0
0 = 0 , verificat
2) f( x) = 2012x - 2011
A( 2013/2012, 2) ∈ Gf ⇒ f( 2013/ 2012) = 2, calculezi f ( 2013/2012)
f ( 2013/2012) = 2012 · 2013/2012 - 2011
= 2013 - 2011
= 2
DECI VERIFICA RELATIA.
3) SUBMULTIMI:
B = { a,b,c}
C = { a,d,e}
E = { b,c,d}
4) ECUATIA EXPONENTIALA:
4^x - 10·2^x+ 16 = 0
2^2x - 10· 2^x + 16 = 0
se noteaza 2^x = y
y² - 10y + 16 = 0, ecuatie de gr. II
a = 1, b = - 10, c = 16
delta = b² - 4ac
delta = ( - 10)² - 4·1·16 = 100 - 64 = 36
delta = 36 ( > 0)
y1 = - b - √delta / 2a = 10 - √36 / 2 = 10 - 6 / 2 = 4/2 =2
y1 = 2
y2 = - b + √delta / 2a = 10 + √36 / 2 = 10 + 6 /2 = 16/2 = 8
y2 = 8
2^x = y1
2^x = 2 ⇒ x = 1
2^x = y2
2^x = 8 ⇒ 2^x = 2^3 ⇒ x = 3
DECI ECUATIA ARE DOUA SOLUTII : X = 1 SI X = 3
