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Answers
Answer:
SO 7.5 ANS
Step-by-step explanation:
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Topic
Linear Equations
Given
The numerator of a fraction is multiple of two numbers. One of the numbers is greater than the other by 2. The greater number is smaller than the denominator by 4.
To Find
Options which could not be the value of the fraction.
Solution
Let smaller number of numerator be 'x'.
then
other number will be 'x+2'
Let denominator be 'y'.
It is given that,
y = ( x + 2 ) + 4
y = x + 6
So, fraction will be
x(x+2) / ( x + 6 )
( x² + 2x ) / ( x + 6 )
Now,
Checking options
i) 5 / 7
( x² + 2x ) / ( x + 6 ) = 5 / 7
7( x² + 2x ) = 5( x + 6 )
7x² + 14x = 5x + 30
7x² + 9x - 30 = 0
D > 0
So, x will exist.
ii) 7 / 5
( x² + 2x ) / ( x + 6 ) = 7 / 5
5( x² + 2x ) = 7( x + 6 )
5x² + 10x = 7x + 42
5x² + 3x - 42 = 0
D > 0
So, x will exist.
iii) - 10
( x² + 2x ) / ( x + 6 ) = - 10
x² + 2x = -10(x + 6)
x² + 12x + 60 = 0
D < 0
So, x will not exist.
iv) - 1 / 10
( x² + 2x ) / ( x + 6 ) = -1 / 10
10( x² + 2x ) = -( x + 6 )
10x² + 21x + 6 = 0
D > 0
So, x will exist.
Answer
So, option which could not be the value of the fraction is option C.