Question

The difference between the square of a number and four times the number is 45 what are the numbers?

Answer 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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Answer 2

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