दो क्रमिक विषम संख्याओ का गुअनंफल 143 है समीकरण बनाये?
Answers
Answer:
Required pairs of the satisfactory odd consecutive numbers are ( 11 , 13 ) and ( - 13 , - 11 ) .
Step-by-step explanation:
Let the required two odd ( विषम ) consecutive ( क्रमिक ) numbers are 2n + 1 and 2n + 3.
Given,
Product of those of two odd ( विषम ) consecutive numbers is 143.
= > ( 2n + 1 ) x ( 2n + 3 ) = 143
= > 2n( 2n + 3 ) + 1( 2n + 3 ) = 143
= > 4n^2 + 6n + 2n + 3 = 143
= > 4n^2 + 8n + 3 - 143 = 0
= > 4n^2 + 8n - 140 = 0
= > 4[ n^2 + 2n - 35 ] = 0 { 4 ≠ 0 }
= > n^2 + 2n - 35 = 0
= > n^2 + ( 7 - 5 )n - 35 = 0
= > n^2 + 7n - 5n - 35 = 0
= > n( n + 7 ) - 5( n + 7 ) = 0
= > ( n - 5 )( n + 7 ) = 0
Since the product of these numbers is 0, one of these numbers must be equal to 0.
If n - 5 = 0
n = 5
If n + 7 = 0
n = - 7
Taking n - 5 = 0
Numbers are :
2( 5 ) + 1 or 11 and 2( 5 ) + 3 or 13.
Taking n + 7 = 0
Numbers are :
2( - 7 ) + 1 or - 13 and 2( - 7 ) + 3 or - 11 .
Required pairs of the satisfactory odd consecutive numbers are ( 11 , 13 ) and ( - 13 , - 11 ) .