Question

4. Calculaţi: x - y - z, x+y-z şi-x - y + z, unde x = a + b -c, y = a-b-c şi
z=-a-b+c, iar:
a) a=5√5-3√2+2√3, b=√√5-4√√2-3√3, c= 2√5-√3-5√2;
b) a=6√5-5√√2-4√3,b=3√5-4√2-6√3,c= -√5 +2√3-6√2;
c) a = 4√5-7√√2-3√3, b=-2√5 +5√2-7√3,c=-3√5-3√2-5√3.

Answer 1

Răspuns: Salut!

a) x - y - z = a + b - c - (a - b - c) - (-a - b + c) = 0;

x + y - z = (a + b - c) + (a - b - c) - (-a - b + c) = 2a;

-x - y + z = -(a + b - c) - (a - b - c) + (-a - b + c) = -2a.

b) x - y - z = (6√5-5√√2-4√3)-(3√5-4√2-6√3)-(-√5 +2√3-6√2) =

= 9√5-9√√2-14√3+6√2-√5+2√3-6√2 =

= 9√5-9√√2-14√3+8√2-2√3 =

= 9√5-9√√2-14√3+8√2-2√3 =

= (3√5-3√2-5√3)-(-2√5 +5√2-7√3)-(-3√5-3√2-5√3) =

= 6√5-8√2-12√3+5√2+3√2+5√3 =

= 6√5-3√2

c) x - y - z = (4√5-7√√2-3√3) + (-2√5 +5√2-7√3) + (3√5-3√2-5√3) = -5√2 - 3√3

x+y-z = (4√5-7√√2-3√3) + (-2√5 +5√2-7√3) + (-3√5-3√2-5√3) = -5√5 - 3√3

-x - y + z = -(4√5-7√√2-3√3) + (2√5 -5√2+7√3) + (3√5-3√2-5√3) = 5√2 - 3√3

a+b+c = 4√5-7√√2-3√3 - 2√5 +5√2-7√3 - 3√5-3√2-5√3

a+b+c = 4√5-7√√2-3√3 - 2√5 +5√2-7√3 - 3√5-3√2-5√3

a+b+c = -10√5 +12√2-13√3

a = 4√5-7√√2-3√3

b = -2√5 +5√2-7√3

c = -3√5-3√2-5√3

Explicație pas cu pas:

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