Q. 74.2( 18 Votes )
The difference of squares of two numbers is 180. The square of the smaller number is 8 times the larger number. Find the two numbers.
Answer :
18, 12; - 18, - 12
Let the larger number be x and smaller number be y
x2 – y2 = 180 …Equation (i)
Since the square of the smaller number is 8 times the larger number, so
⇒ x2 – 8x - 180 = 0
Performing factorization we get:
⇒ x2 - 18x + 10x - 180 = 0
⇒ x(x - 18) + 10(x - 18) = 0
⇒ (x + 10)(x - 18) = 0
x = - 10,18
Rearranging Equation (i)
y2 = x2 - 180
Putting x = - 10 we get
y2 = - 80
Since the square is negative so the solution is neglected
Putting x = 18 we get
y2 = 144
⇒ y = 
12
Answer: 18,12 ;18, - 12
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