Question

Solve this question...

• The difference of squares of two natural number is 45. The square of smaller number is four times the larger number. Find the numbers..​

Answer 1

Let the number be p and y

According to the Question

p^2 - y^2 = 45

y^2 = 4p

p^2 - 4p = 45

p^2 - 4p - 45 = 0

p^2 - 9p - 5p - 45 = 0

p(p - 9) - 5(p - 9) = 0

p = 9 and 5

y^2 = 4p

= 4 × 9

= 36

y = 6

y^2 = 4 × 5

= 45

p = 9 and y = 6

Answer 2

Suppose, one number be x and other be x+1.
so as per question,( x +1)^2 - x^2=45.......(1)
and x^2=4(x+1)..............(2)
Now, (x+1)^2 - 4(x+1)=45
or, x^2+2x+1-4x-4=45
or, x^2 -2x-48=0
or, x^2 -8x+6x-48=0
or,x(x-8)+6(x-8)=0
or,(x-8)(x+6)=0
or,x=8 or -6
Here we take x=8 so other number is 9.