Page 43 - Start Up Mathematics_8 (Non CCE)

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1 − ()  − 1 (−1 ) 16 16
⇒ = ÷   = × = = 4
x 4  16  4 (−1 ) 4
1 1
⇒ = 4 ⇒ x =
x 4

 9  − 5  2  − 3
Example 11: Find the reciprocal of   ÷   .
 2   9 

n
 9  − 5  2  − 3  2  5  9  3   x  − n  y  

Solution:   ÷   =   ÷       =   
 2   9   9   2       x  
y

 2  5  2  3
=   ×  
 9   9 
 2  5 + 3  2  8
n
m
=   =   { (x) × (x) = (x) m + n }
 9   9 
 2  8 1  2  − 8  9  8
So, reciprocal of   = =   =  
 9   2  8  9   2 
 
 9  Try It Out!

 2 −3  2 11  2 3x + 2 Solve the given expression
− 
− 
− 
Example 12: Find the value of x if   ×   =   .
 5   5   5  mentally. 1 − 1 − 1 −
1
− 
 2 −3  2 11  2 3x + 2  1 +    +  1
− 
− 
 
 
Solution:   ×   =    4  3  2
 5   5   5 
 2 −+3 11  2 3x + 2
− 
− 
m
n
⇒   =   { (x) × (x) = (x) m + n }
 5   5 
− 
 2 8  2 3x + 2
− 
⇒   =  
 5   5 
m
n
⇒ 3x + 2 = 8 { If (x) = (x) ⇒ m = n}
⇒ 3x = 8 – 2 = 6
6
⇒ x = = 2
3
So, x = 2
p  2  − 2  2  − 1  p  −3
Example 13: If q =   ÷   ,(q ≠ 0), find the value of  q   .
3 

5 



n
p  2  − 2  2  − 1  3  2  5  1   x  − n  y  

Solution: q =   ÷   =   ÷       =   
y

x 

2 

3 

5 
2 

 
 
 
×
×
 3  2 2 3 () 2 2 92 91 9 p 9
=   × = × = = = ⇒ =
×
×
 2  5 2 () 2 5 45 25 10 q 10

n

 p  −3  9  −3 10  3 1 000,   x  − n  y  
So,   =   =   =     =   
y
 q   10   9  729      x   
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