Odpowiedź:
a) :
√3(x + √3) = -3
x√3 + 3 = -3
x√3 = -3 - 3
x√3 = -6 /:√3
x = -6 : √3 = -6/√3 = -6/√3 * √3/√3 = -6√3 : 3 = -2√3
b)
x√8 + √2 = √18 - √2x
x√8 + x√2 = √18 - √2
x(√8 + √2) = √(2*9) - √2
x[√(4*2) + √2] = 3√2 - √2 *
x(2√2 + √2) = 2√2
x * 3√2 = 2√2 /:3√2
x = 2/3
c)
2(√5x - 4) = x√80 + 2
2√5x - 8 = x√(16*5) + 2
2√5x - 8 = 4√5x + 2
2√5x - 4√5x = 2 + 8
-2√5x = 10 /:(-2√5)
x = -5/√5 = -5/√5 * √5/√5 = -5√5 : 5 = -√5
d)
2/3(x√27 - 1 2/3) = 2(√3x - 1)
2/3[x√(9*3) - 1 2/3) = 2x√3 - 2
2/3(3x√3 - 5/3) = 2x√3 - 2
2x√3 - 10/9 = 2x√3 - 2
2x√3 - 2x√3 = -2 + 1 1/9
0 = -8/9
rownanie sprzeczne
e)
√2(x + 5) + 2x = 2(x - √18)
x√2 + 5√2 + 2x = 2x - 2√(9*2)
x√2 + 2x - 2x = -2*3√2 - 5√2
x√2 = -11√2 /:√2
x = -11
f)
2(√12x - 1) = -4(0,5 - √3x)
2√12x - 2 = -2 + 4√3x
2√(3*4)x - 4√3x = -2 + 2
2*2√3x - 4√3x = 0
4√3x - 4√3x = 0
0 = 0
rownanie tozsamosciowe
Szczegółowe wyjaśnienie:
