Question -
Answer -
Let us say, the larger and smaller number be x and y respectively.
As per the question given,
x2 – y2 = 180 and y2 =8x
⇒ x2 – 8x = 180
⇒ x2 – 8x – 180 = 0
⇒ x2 – 18x + 10x –180 = 0
⇒ x(x – 18) +10(x – 18)= 0
⇒ (x – 18)(x + 10) = 0
⇒ x = 18, -10
However, the larger number cannot consideredas negative number, as 8 times of the larger number will be negative and hence,the square of the smaller number will be negative which is not possible.
Therefore, the larger number will be 18 only.
x = 18
∴ y2 = 8x = 8 × 18 = 144
⇒ y = ±√144 = ±12
∴ Smaller number = ±12
Therefore, the numbers are 18 and 12 or 18 and-12.