Question

The difference between squares of two numbers is 45, the square of smaller number is 4 times the larger number. Find the numbers

Answer 1

13 answers · Mathematics

Best Answer
Let larger no. be x
& smaller no. be y

so, A to Q
x^2 - y^2 = 45 .......(i)
y^2 = 4x .......(ii)

Now putting y^2 = 45 in eq. (i)

x^2 - 4x = 45
x^2 - 4x - 45 = 0
x^2 - 9x + 5x - 45 =0
x(x-9) + 5(x-9) = 0
(x-9) (x+5) = 0
x = 9 & x = -5
but Square of any no. can never be -ve.
so, x = 9
putting x = 9 in eq. (ii)
y^2 = 4(9) = 36
y = 6

Ans. Hence, the two nos. are 9 and 6