find the two numbers whose sum is 27 and product is 182
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Answered by
5
Let the one number be x.
Another number will be ( 27 - x ).
A.T.Q.
( x ) ( 27 - x ) = 182
27x - x² = 182
x² - 27x + 182 = 0
By Middle Term factorisation
x² - 14x - 13x + 182 = 0
x ( x - 14 ) - 13 ( x - 14 ) = 0
( x - 14 ) ( x - 13 ) = 0
Using Zero Product Rule
x - 14 = 0 and x - 13 = 0
x = 14 and x = 13
: When x = 14
One number = x = 14
Another number = 27 - x = 27 - 14 = 13
: When x = 13
One number = x = 13
Another number = 27 - x = 27 - 13 = 14
Hence,
Another number will be ( 27 - x ).
A.T.Q.
( x ) ( 27 - x ) = 182
27x - x² = 182
x² - 27x + 182 = 0
By Middle Term factorisation
x² - 14x - 13x + 182 = 0
x ( x - 14 ) - 13 ( x - 14 ) = 0
( x - 14 ) ( x - 13 ) = 0
Using Zero Product Rule
x - 14 = 0 and x - 13 = 0
x = 14 and x = 13
: When x = 14
One number = x = 14
Another number = 27 - x = 27 - 14 = 13
: When x = 13
One number = x = 13
Another number = 27 - x = 27 - 13 = 14
Hence,
Answered by
1
Answer:
13+14=27
13×14=182
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