Questions Based On Algebraic Identities class 8
Questions Based On Algebraic Identities
Exercise
1. If ( x + 1/x ) = 4 , find the valves of :
i) ( x - 1/x)
ii) (x² + 1/x² )
iii) ( x4+ 1/x4)
i) ( x - 1/x)
( x + 1/x ) = 4
squaring both side
( x + 1/x )2 = 42
(x)² + (1/x)² + 2* x * 1/x = 16
x² + 1/x² + 2 = 16
x² + 1/x² - 2 + 4 = 16
x² + 1/x² - 2 = 16 - 4
( x - 1/x )2 = 12
( x - 1/x ) = √12
( x - 1/x ) = ± 2√3
ii) (x² + 1/x² )
( x + 1/x )2 = 42
(x)² + (1/x)² + 2* x * 1/x = 16
x² + 1/x² + 2 = 16
x² + 1/x² = 16 - 2
x² + 1/x² = 14
iii) ( x4+ 1/x4)
x² + 1/x² = 14
squaring both side
(x²)² + (1/x²)² + 2* x² * 1/x² = 14²
x4 + 1/x4 + 2 = 196
x4 + 1/x4 = 196 - 2
x4 + 1/x4 = 194
2. If ( z - 1/z ) = 6 , find the valves of :
i) ( z + 1/z)
ii) (z² + 1/z² )
iii) ( z4+ 1/z4)
i) ( z + 1/z)
( z - 1/z ) = 6
squaring both side
( z - 1/z )2 = 62
(z)² + (1/z)² - 2*z * 1/z = 36
z² + 1/z² - 2 = 36
z² + 1/z² + 2 - 4 = 36
z² + 1/z² + 2 = 36 + 4
( z + 1/z )2 = 40
( z + 1/z ) = √40
( z + 1/z ) = ± 2√10
ii) (z² + 1/z² )
( z - 1/z )2 = 62
(z)² + (1/z)² - 2* z * 1/z = 36
z² + 1/z²- 2 = 36
z² + 1/z² = 36 + 2
z² + 1/z² = 38
iii) ( z4+ 1/z4)
z² + 1/z² = 38
squaring both side
(z²)² + (1/z²)² + 2* z² * 1/z² = 38²
z4 + 1/z4 + 2 = 1444
z4 + 1/z4 = 1444 - 2
z4 + 1/z4 = 1442
3. (a² + 1/a²) =23, find the value of (a + 1/a).
(a² + 1/a²) =23
Adding 2 both side
a² + 1/a² + 2 = 23 + 2
a² + 1/a² + 2 = 25
( a + 1/a )2 = 52
( a + 1/a ) = ± 5
4. (x² + 1/x²) = 102 , find the value of (x - 1/x).
(x² + 1/x²) = 102
Subtracting 2 both side
x² + 1/x² - 2 = 102 - 2
x² + 1/x² + 2 = 100
( x - 1/x )2 = 1002
( x - 1/x ) = ± 10
5. a + b = 8 and ab = 15 , find the value of (a² + b² )
a + b = 8
( a + b )2 = 82
a² + b² + 2ab = 64
a² + b² + 2*15 = 64
a² + b² + 30 = 64
a² + b² = 64 - 30
a² + b² = 34
6. If a + b = 11 and (a² + b² ) = 61 , find the value of ab
a + b = 11
( a + b )2 = 112
a² + b² + 2ab = 121
61 + 2ab = 121
2ab = 121 -61
2ab = 60
ab = 60/2
ab = 30
7. If a² + b² = 13 and ab = 6 , find the value of (a + b ) .
(a + b )² = a² + b² + 2ab
(a + b )² = 13 + 2 * 6
(a + b)² = 13 + 12
(a + b) = ± 5
8. Find the value of :
i) 36x² + 49y² + 84xy, when x = 3, y = 6.
36x² + 49y² + 84xy = ( 6x + 7y)2
= (6*3 + 7*6)2
= (18 + 42)2
= 602
= 3600
ii) 25x² + 16y² - 40xy, when x = 6, y = 7.
25x² + 16y² - 40xy = ( 5x - 4y)2
= (5*6 - 4*7)2
= (30 - 28)2
= 22
= 4
Post a Comment