If ax2 + bx + c = 0, then x
= (-b + sqrt(b2 – 4ac))/2a.
(where a, b, c are constants & a
not equal to 0)
axay = ax
+ y a1/x
= x√a
(ax)y = axy ax/y = y√ax
(ab)x = axbx ax/y
= ( y√a)x
(a/b)x = ax/bx x√ab
= x√a x√b
ax/ay = ax-y
x√(a/b)
= x√a/x√b
a-x = 1/ax x√y√a
= xy√a
|x| < a if and only if
-a<x<a
|x| > a if and only if either x>a or x<-a
(x + y)(x – y) = x2 – y2
(x + y) 2 = x2 +
2xy + y2 (x – y)
2 = x2 – 2xy + y2
(x + y)3 = x3 +
3xy2 + 3xy2 + y3 (x – y) 3 = x3 – 3xy2 + 3xy2
– y3
(x + y)n = x n +
(n1)x n-1 y + (n2)x
n-2 y 2 + ... + (nk)x n-k y
k + ... + y n,
where (nk) =
n!/k!(n – k)!
X2 – y2 = (x +
y)(x – y)
x2 + 2xy + y2 =
(x + y)2 x2
– 2xy + y2 = (x – y) 2
x3 – y3 = (x –
y)(x2 + xy + y2) x3
+ y3 = (x + y)(x2 – xy + y2)
If a>b and b>c, then a>c.
If a>b, then a+c>b+c.
If a>b and c>0, then ac>bc.
If a>b and c<0, then ac<bc.
y = logax ó ay = x logaxy = logax
+ logay
loga (x/y) = logax
– logay logaxr
= rlogax
alogax = x logaax
= x
loga1 = 0 logaa
= 1
logx = log10x lnx = logex
logbu = logau/logab