The difference between the square of a number and four times the number is 45 what are the numbers?
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Answered by
1
ANSWER
Let the two numbers be a and b
a
2
−b
2
=45.............................(1)
b
2
=4a..............................................(2)
Putting (2) in (1)
a
2
−4a=45
a
2
−4a−45=0
a
2
−9a+5a−45=0
a(a−9)+5(a−9)=0
(a−9)(a+5)=0
a=9ora=−5
If a=5, b=25−b
2
=45
25−45=b
2
b
2
=20(Neglecting this value)
IF a=9 81−b
2
=45
81−45=b
2
b
2
=36
b=±6
Numbers are 9,6 or 9,-6
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Answered by
0
Let the no be x
So square of number is x^2
And 4times the no is 4x and their difference is 45
X^2 - 4x = 45 ——-> 1
X^2 - 4x - 45 = 0
Product of no is -45 and sum is -4
Therefore the nos are -9 and 5
Equation 1 can be written as
X^2 - 9x + 5x - 45 = 0
X( x - 9 ) + 5 ( x - 9 ) = 0
Thereby we get
X-9 = 0 and x + 5 = 0
So the numbers are 9 and -5
So square of number is x^2
And 4times the no is 4x and their difference is 45
X^2 - 4x = 45 ——-> 1
X^2 - 4x - 45 = 0
Product of no is -45 and sum is -4
Therefore the nos are -9 and 5
Equation 1 can be written as
X^2 - 9x + 5x - 45 = 0
X( x - 9 ) + 5 ( x - 9 ) = 0
Thereby we get
X-9 = 0 and x + 5 = 0
So the numbers are 9 and -5
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