Question

The difference of the squares of two positive intigers is 180. The square of smaller number is 8 times the larger

Answer 1

Let the two positive integers are 'x' and 'y'.

Now according to the first condition , we get:

the difference of their squares

is 180.

x2-y2=180...............(1)

Also according to the second condition , we get:

the square of the smaller

number is 8 times the larger

number.

y2=8x...................(2)

Put equation (2) in equation (1) , we get:

x2-8x=180

x2-8x-180=0

Here, a=1

b=-8

c= -180

Now, discriminant=b2-4ac

=-8×(-8)-4×1(-180)

=64+720

=784.

Therefore , the given quadratic equation has real and unequal roots .

Now by using quadratic formula , we get:

x=-b plus minus √D

2a

x=-(-8) plus minus √784

2×1

x=8 plus minus 28

2

x=8+28 , 8-28

2. 2

x= 18 , -10.

Put x=10 in equation (2) , we get:

y2=8×(-10)

y2=-80

which is not possible because square of any real number can never be negative.

So, we reject x=-10.

Put x=18 in equation (2) we get:

y2=8×18

y2=144

y=√144

y=√12×12

y=12.

Two no's. are 18 and 12.

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