Question

7.Z każdego z poniższych wzorow wyznacz k.
a)a=xk+yk

b)b=2k-ak

c)c= (k + 1)b+sk

d)d=k/k-1

e) e= k-1/k+1

f) k=k+1/k + a

g) g = 2 -1/k

i) i= a/2 + 2/k

Answer 1

A)a=xk+yk
a=k(x+y)
k(x+y)=a
k=a:(x+y)

b)b=2k-ak
2k-ak=b
k(2-a)=b
k=b:(2-a)

c)c= (k + 1)b+sk
(k + 1)b+sk=c
kb+b+sk=c
bk+sk=c-b
k(b+s)=c-b
k=(c-b):(b+s)

d)d=k/k-1 /*(k-1)
d(k-1)=k
dk-d=k
dk-k=d
k(d-1)=d
k=d:(d-1)

e) e= k-1/k+1 /*(k+1)
e(k+1)=k-1
ek+e=k-1
ek-k=-1-e
k(e-1)=-1-r
k=(-1-e):(e-1)

f) k=k+1/k + a /*k
k²=k²+1+ak
k²-k²-ak=1
-ak=1
k=1/(-a)

g) g = 2 -1/k /*k
gk=2k-1
gk-2k=-1
k(g-2)=-1
k=-1/(g-2)

i) i= a/2 + 2/k /*k
ik=ak/2+2
ik-½ ak=2
k(i-½a)=2
k=2/(i-½a)

Answer 2

A)a=xk+yk
a= k (x+y) / : (x+y)
a / (x+y) = k
k = a/ (x+y)

b)b=2k-ak
b = k(2-a) / : (2-a)
b / (2-a) = k
k = b / (2-a)

c)c= (k + 1)b+sk
c = bk+ b+ sk
c-b = k (b+s) / : (b+s)
(c-b) / (b+s) = k
k= (c-b) / (b+s)

d)d=k/k-1 / * (k-1)
d (k-1) = k
dk - d = k
dk-k = d
k (d-1) = d / :(d-1)
k = d / (d-1)

e) e= k-1/k+1 / *(k+1)
e * (k+1) = k-1
ek +e = k-1
ek-k = -1-e
k (e-1) = -1-e / : (e-1)
k = (-1-e )/ (e-1)

f) k=k+ 1/k + a / *k
k² = k² +1+ ak
k²-k² -ak = 1
-ak = 1 / :(-a)
k = 1 / -a

g) g = 2 -1/k / * k
gk = 2k -1
gk-2k = -1
k (g-2) = -1 / :(g-2)
k = -1 / (g-2)

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