Question

Z kazdego z ponizszych wzorów wyznacz k

a) e = k-1/k+1

b) h = ka do potęgi 2 + k

c) i = a/2 + 2/k

Answer 1

A)
e = k-1/k+1 |*(k+1)
e(k+1) = k-1
ek+e+1 = k
ek-k = -e-1
k(e-1) = -e-1
k(e-1) = -(e+1)
k = -(e+1)/e-1)

b)
h = ka²+k
h-ka² = k
-ka²-k = -h |*(-1)
ka²+k = h
k(a²+1) = h
k = h/a²+1)

c)
i = a/2+2/k |*2k
2ki = ak+4
2ki-ak = 4
k(2i-a) = 4
k = 4/(2i-a)

Answer 2

A)
e = k-1/k+1
e(k + 1) = k - 1
ek + e = k - 1
ek - k = - (e + 1)
k(e - 1) = -(e + 1)
k = -(e + 1)/(e - 1)
b)
h = ka do potęgi 2 + k
h = ka² + k
h = k(a² + 1)
k = h/(a² + 1)
c)
i = a/2 + 2/k
2ki = ak + 4
2ki - ak = 4
k(2i - a) = 4
k = 4/(2i - a)