Question

Calculati:
a) (5√2 - 3√2)x + (6√2 - 4√2)x - (7√2 - √2) x + 4√2x
b) (2√20 + √80)xy - √45xy + √125xy + (√5 + √180)xy
c) √6x^2 + (√192 - √54) x^2 + 2√150x^2 + 7√3x^2 - 2√75x^2

Se considera numerele A= a^2 + x + 2, B= 3a^2 + 2x - 7, C= 4x + 12
Calculati:
a) A+B
b) A-B
c) A+B+C
d) A+(B-C)
e) -A+B-C
f) (A-B)+(B-C)+(C-A)

Answer 1

a) (5√2 - 3√2)x + (6√2 - 4√2)x - (7√2 - √2)x + 4√2x=
 = 2√2x + 2√2x - 6√2x + 4√2x =
 = 4√2x - 6√2x + 4√2x =
 = -2√2x + 4√2x =
 = 2√2x
b) Aici va trebui mai intai sa scoti de sub radical, descompunandu-le mai intai in factori primi.
 
20:2 = 10: 2 = 5:5 = 1
Deci vom avea 2√5 
Si cum noi avem deja doi in fata radicalului, vom obtine: 2 X 2√5 = 4√5
80:2 = 40:2 = 20:2 = 10:2 = 5:5= 1 => √80 = 4√5
45:5= 9:3 = 3:3 = 1 => √45 = 3√5
125:5 = 25:5 = 5:5 = 1 => √125= 5√5
180:2= 90:2 = 45:5 = 9:3 = 3:3 = 1 => √180 = 6√5