Page 47 - WCS - Electrical
P. 47
WORKSHOP CALCULATION & SCIENCE - CITS
x + y = 16 + 24
2
2
x + y 2 = 40
2
4 If x - y = 7 and xy = 60 then find the value of x + y 4
4
(x - y) 2 = x + y - 2xy = 7
2
2
2
x + y - 2 x 60 = 49
2
2
x + y = 169
2
2
(x + y ) = (169) (take square on both side)
2
2 2
2
x + y + 2x y = (169) 2
2 2
4
4
x + y + 2(xy) = 28561
4
2
4
x + y + 2(60) = 28561
4
2
4
x + y + 2(3600) = 28561
4
4
x + y + 7200 = 28561
4
4
x + y 5 = 28561 - 7200
4
4
3
x + y 5 = 21361 = x − 1 - 1 2 + 1 = 16 + 2
4
4
−x
3
5 x + y = ; x - y = Find the value of 8 x y (x + y ) 1 = x − 1 x 3 - −x x 1 x x 2 + 1 x 2 = 16 + 2
2
2
5
3
3
x
x + y = ; x - y = (take square on both sides) = x − 1 3 - −x 1 3 1 x 1 x 2 + 1 = 16 + 2 x 2
3
5
2
1
3
3
−
2
=
3
3
(x + y) = 5; (x - y) = 3 2 = x − x 3 - 2 = x 1 x 1 x 3 -3 −x x 1 x 2 + 1 2 = 16 + 2 1
2
−x
x
4 1
2
3
3
x
2 3
Solve the equations = 1 2 2 = x − 1 2 = x x − 13 -3 −x x x 2 x 2 + 1 2 = 18
1
4
3
3
x
-3 −x
=
8
2 x
2 4 x
(x + y) = 24 1 x + y + 2xy = 5 2 = x − 1 3 3 x 1 1 x 2 + x 2 = 18
2
2
1
2
x
1
3
3
8 = x −
2 x
x
2 4
(x - y) = 24 = 1 8 x + y - 2xy = 3 x 3 -3 −x x 1 3 -3( ) 2 x 2 + = 18 x
2
1
2
3
8 x x 4 − 8 = x − x -3( ) 2 2 + 1 2 = 18 1 2
x
a
---------------------------------------- 3 1 3 x 2 x 2 − = (18)
a
2
2 1
1
a
8 x x 4 − 2 8 = x − -3( ) 2 x x 2 2
2 1 2 (x + y ) = 8 3 1 3 1 2 x − 1 x = (18)
2
a
2
2
x
a
−
8 = x −
2
2
2
2
2
(x + y ) = = 4 a + 1 8 = x − 3 -3(2 3 ) -6 2 − 1 = (18)
a 1
x
x
2
a
− 2 1 a 2 x 8 = x − 1 x 3 -6 1 2 2
3
x
2
a 1 a + 2 3 1 -6 x 3 x − = (18) 1 1
2 2
2 a
a 2 = + x + y + 2xy = 5 5 8 = x − x 1 2 (x ) + 1 + 2 x x 2 x = 324
2
3
1 2 a 1 2 8 = x − 1 3 -6 = x − - 2 2 −x 1 2 1 2 2 1
x
3
a
2 −
(x )
a 2 = + x + y - 2xy = 3 3 8+6 = x − 1 x 3 1 + x x 2 x 2+ x 2 x x = 324 +x 2 = 16 + 2
3
a
1
1
2
a
2 2
−
a
(-) (-) (+) (-) 3 3 1 1 x 8+6 = x − 1 x 3 (x ) + 1 1 + 2 x x x 2 x 1 2 = 324 x 2 x
5 5
2
1
3
a
1 1
x
5
a
3
1
=
x 1 1
3
2 2 3
+ -3
-------------------------------------------
2 =
x −
− a 1 1 2 2 = 1 = x − x − 3 - 3 3 −x - 3 −x 1 1 x 3 (x ) 2 + x − 2 16 = = 2 + 1 1 2 6 + 2 1 1 = 324
x x x
8+6 = x −
2
2
+
-
x
+ x
− 3 5 3 a − 2 4 2 x x = x − x x −x 2 x 2 x 2 4 + 16 = x x + + 2 2 = 324
2
a
3
x +
3
13
a 3 1 5 a 4xy = 2 = x − 1 - 3 x x 1 3 1 1 x 1 x x x 2 1 4 x 2 + 1 = 18
8+6 = x −
3
a
2 −
3
3 = x −
4x
2 1
324
−x
x
1 1
1
2 1 12 ------------------------------------------- 1 3 3 3 3 3 1 1 14 = x − - −x x 2 + 1 = 16 x + + 2 x + = = 16 + 2 2
2
a
1
2 =
x
-3 −x −x
3 5 a − 2 1 8 x x 4 2 = x − x x − 3 -3 x 3 1 3 1 x 3 1 x 4 + 1 + 2 = 324 4 + x
= =
x
x
14 = x −
2
3
x
3
2
3 x
xy 4 4 a − 1 2 2 = 3 2 = x − 1 2 = x − 3 x -3 −x 3 x 8 = x − 1 1 1 ) 4 + 1 x 2 = 324 2 −
3
x
= a
4 -3(2
2
3
x x
1 1
x
14 = x − -
3
x 1
+ + 1
2
4
x
4 2
1
= =
x
2 18 18
+ 3
1 −x
=1
2
2
1
2
1
2
2 a
3
1
3
a
2 = x −
2 1 1
3 3
3
4 =
=
8 xy (x + y ) a 4 2 1 + = 8 x x 4 1 − a 3 14 = x − 3 1 -3 3 x − x 1 3 1 1 3 1 x x x 2x + + x x x 2x x 1 = 2 6 + + x 2 324 1 18 4 = 324 2 − x 2 − 1 2 = (18)
2
x 2 = x − −xx
4 x
x
2
=
= 14 -3 −x
x
x
− (a) 2
x
8 x 8
4 x
3
+
3
2
4
2
2
2
a 4
x
a
1 x
4
1
x
8
x
x
4
3
3
8 =
x x − ) ( ) 2
2
-3(2 -3
324
=
−
2 a 2
3
=
2 2 2 x + = 4 x 4 = 16 (a) 2 1 8 = x − x − 1 1 -3 3 3 3 1 1 x = 14 x 2 x + 4 1 + = 1 4 1 18 x x 4 2 + + x 1 2 − 1 = 18 x 2
2
1 1
a
-3( ) 2
1
3
3
1 1 1
1
a
3
= 14
1 3
2 = x −
2
322
3 8 = x − −x
-6
3
1 2 2
x
4
a8
4 x
x
8 = x −
x
2
1 8
324
+
=
a
−
= 6. Find the value of a + +
6 If 4 + a x = − x − (a) 2 2 1 2 4 x a 2 2 1 x − x x x x 4 1 1 2 x 1 1 4 = (18) (18) 1 2 x 4 2 − 2
1
3
2 2
3
a
2
1
3
x
1 1 x
2
a
a 1
3
−
2
+
x1 =
a a
2
x
− 1 −
x
4
x − x −
-3
3 3
322
=
a
2
x
2
+
8 = x −
− (a) 2
a 1 1 2 a + 2 − 2 = 36 a 2 8 = x x − − 3 3 = 14 ( ) 2 x 1 3 3 1 -3( ) 2 x x + 4 x 2x x 18 = 2 − x 4 = (18)
2
2
1 x
2
a
4
a
a 1
322
4
+
− x 4 a = 6 1 − 2 = 36 8 = x 8 = 3 3 x x 1 1 x − x − x x x x + 1 = 2 1 2 (x ) + 1 + 2 x x 2 x 1 = 324
8
a x
a
2 2
2
−
x
1 1
1
-6 -6
1− x −
1 x 1
2 + a
a 2 + 1 2 − 2 1 36 a 2 a a 1 8 = x − 1 8 = x − ) 1 -6 x 4 x 2 x 4 − + 4 = 322 − = (18) 2 2
2
x = (18)
2
a +
2
2
4
3
a
3
-3(2
x
=
3
−
x − x − 3
2
2 a a 2 a + =6 (take square on both sides) x 1 x x 1 4x − = 4 8+6 = 2 x x − 1 x 2 x x
1
4 3
x
1
3
3
a
2
1
x
2
4
x 1 x
x − x −
a a + − 1 a − 2 2 + 36 1 = 36 + 2 8 = x − x 1 -6 4 x − = 4 1 -6 2 2 2 2 2 3 2 1 1
2a
1
a =
3
11
3
2
x
a + a
2
(
2
1 1 a 2 2 a + a 2 x 1 3 x 8 = x − 2 3 (x ) x +x ) + − 2 + 2 =2+ x x x 2 2 = 324 324= 1
1
1 (18) x x x
x
(x ) 2 2
2
2 2
2
2
x
2
x x
− a 1 a 1 + a = 36 + 2 1 2 x − = 4 1 1 1 x x x + 2 + x x 2 x = 324
2
−
a a
3
3
8+6 =
a a a a = − 36 2 + 2 1 a 2 a − 8+6 = x 1 x − 1 x − −x 3 2 2 x x 2 1 1 x 2 1 x 4 + 1 + 2 = 324
2
+ 1
2 1
1
3
x − = 4 3 -6
8 = x −
2
2 2
(x )
x −
=
a
2
+
a + 1 2 a + 1 a x 8+6 = 3 x 1 (x ) + 2 + 1 2 x x + x 2 324 x x 2 x = 324 4
2 1
a
x x
3
2 1
2 −x
3
x
a
36
+
x
=
a
− a 2 2 2 2 2 + a 2 a 34 1 1 x 3 1 14 = x − 2 x 2
a
x
+ −
x
x
3
2 a 1 1 2 a 2a 8+6 = − 2 8+6 = x − 1 1 1 1 x 3 x
3
1 a
−x x
1
1
x 1
2 2 2
a a − a −
4 4
324
2 3
=
+
−
x
+ 1 1 CITS : WCS - Electrical - Exercise 4 2 x x x x x 1 3 = 4 (x ) x + + + 4 2 2 + 2+ 2 + = x 324x x 1 324 = 2 + 2 2 = 324 x 4 + 1 = 324 2 −
xx
a 1
2 a −
1 a
4
−x
1 1
+
a
1
x 4
2
a
2
1
3
2
14 =
3
x − 3−
1
2
3 x
x x
1
+ 3
a − + 2 2 a x − x 1 1 2 a 2 + 1 14 = 1 14 = x x 1 2 − − 2 1 x x x x = 4 2 4 x − x x 1 = 14 x 4 x 1 x 4
3 −
x
a
1
(a)
− 2
8+6 = x
a
3
a −
3 2 +
+
x x
4
2
+
x
a 1 x − a − a x a − 2 1 3 x x x1 = 3 4 2 1 x 4 x 1 1 = 324 + 4 + 2 = 324
x x x
x a
x
x x −
4 x 4
14 = x −
1 1 1 x 1 1 3 1 x 2 14 = 1 2 3 − 1 1 x x x x 2 1 − 4 2 3 2 = 16 x x + + 324 = = 1 324 2 − − x 2 x 4 + 1 = 322
x − 2
+ =
2
+
2 2
x −
2 1
4
3
1
4
= 14
2 = 14
a
2
2
4
2
1
4 2
x
a a + − a 2 1 (a) 3 2 1 x 3 x 3 2 − x − 3 3 x x − + 1 x1 x = 14 = 16 3 x x − x − x 4 1 324 = + x 4 = 324 2 − x 4
x − − (a) 2 − 2
+
x x
3
+
1 +
x 1
−
2
3
+
x
1
36
2 =
a
x − a a
x
1 3 x
1
a a x a − (a) 2 3 a a + a 2 − 14 = x − − 1 2 = 16 x 3 2 1 4 x+ x 4 1 1 = x 4 324 − 4 2 + 1 = 324 2 −
2
x
3 2
x
+ 1
x
x 2
x
x −
4
3
3
4
3
a 2 + 1 x −x + a (a) 2 1 1 1 3 − 1 1 x) 1 . − 1 x − 1 2 = 14 x − = 14 x x + x + 4 322 = = 1 322 x 4
x
3 −
1
− (3
2
= x− (a) 2
x
2
4
4
2 a 3 a x 1 a 3 a x x 1 x + 1 1 3 4 x − 4 2 = 1 16 1 3 1 x1x x 4 + = 322
x − 1 1
x 1
2
2
x −
36
4
3 2−
a a + + 2 x −x = 136 = = x 3 − 1 x − (3 x) 2 . x 1 x − x − x − 1 4 1 x x − = 4 324 4 2 − 1
2 2−
+
=
1
−
x
x
x
x − x −
+
x
4
4
36
=
x 1 x
4
1
2
3
+
x x
1 x
2
−x − (a) 2
+
a 2 1 1 a a a 2 3 − 1 − − (3 2 x) x . 3 x − 1 x a + x 36 = x − 2 = 14 x 4 x + x 4 4 = 322 x 4 + = 322
x
1
1
= x
a
1
a x 1 1 − 3 2 = a 3 2 1 x 1 x 1 a 2 x − 1 x − x − x − 1 x 2 x 4
3
4
x
2
1
1
+
4
a
x + a 36
=
−
x x −
1
−x 2 = x − − (3 x) 2 − 2 . x 36 1 x − = 4 = 4 4 1 x 4 4 1
−x
1
x
3
2 2 x a 1 = + 3 x 2 2 6 + a x x a 2 + x x x − = 4 x x + x = 322
a a
+ +
=
36
1
2 2 1 2 + = 36 + 2 2 1 1 4 1 x x 4
a + a − a 2 = 36 a x − x − 1
a2
2 2
x − = 4
1 a 2 x 1 1 4 x − = 4
2
a
2 1 1 = 36 + 2 + 2 1 −x −x x x 1 2 x 1 1
a
2 +
2
a a + + 2 1 a 2 = 36 + 2 1 1 x x −x x 2 + − 2 x x x = 4 2
2 a
2
1
a a a 2 2 + a x − x − = 4 x 1 2 x 2 x
1
2 2 + 1 = 36 a 2 1 x −x x −x
a
+
2
a + a 2 2 + 2 1 1 x 1 1 2 x 2
2
x
1 a
a 1 2 1 x x + + − x 2 x x 2− 1 x x = 4 4= 1 2 2 1
2 2
2
2
3
x − x − 1 a x − x x 2 x 1 + 2 − x 2 x x x x = 4 x + − 2 = 16
a 2 + x 1 x x − x 3 2 + −x 1 − x 2 x 1 = 4 12 x 1 2 x 2
2
1 2 x 1 x x x x + − 2 x x x = 4
x
2
3
x − a 1 1 x − 2 x 1 1 x 2 x
2
1 16
3
x − x − 1 x 1 = x 3 x x + 1+ 2 − − 2 = 1 2 =− 16 x 1
x
2
+
3
3 3 x − −x x 2 − 1 x x)( 3 2 2 x x x 2 − . 1 = 2 x 4 = − 2 16
+
3 −
x x
x x
3 x − 1 1 x 3 1 x 2 + x 2 1 − 2 x x 2 1 x
x
16
=
x
3
x − 1 1 x − 1 1 1 1 x 2 x + − 2 = 16
x
1 1
1 x.
3
3
3
3
−x −x x = x = x − 1 − − (3 − x) x)(3 x . − −x 1 1 x x 2
x x −x 3 = x 3 − x x x) x . x − 2 1
− (3
3
1
x
x x
3
x − x 1 1 x 1 1 1 x x 1 + 2 − 2 = 16
x
3
1
1
3
3
−x x = x 3 − −x − (3 x) = x x. − − − (3 x) . x − x
x x 3 x x x 3 x x
x
1 1 1 1
−x = x 3 − − (3 x) . x −
x x 3 x x 
