Question

A difference of square of two numbers in 180.the square of smaller number is eight times the larger number.find the numbers.

Answer 1

Let the numbers be a and b

According to question
b^2 = 8a -------------(1)

a^2 - b^2 = 180
=> a^2 - 8a = 180 (using equation 1)
=> a^2 - 8a - 180 = 0
=> a^2 - 18a +10a - 180 = 0
=> a(a-18) + 10(a-18) = 0
=> (a-18)(a+10) = 0

a= 18 and - 10
Neglecting negative value, we get
a= 18
b= 12

Required numbers are 18 and 12


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Answer 2

let two numbers=x and y
according to question
x^2-y^2=180..................................1
y^2=8x............................................2

x^2-8x=180
x^2-8x-180=0
x^2-18x+10x-180=0
x(x-18)+10(x-18)
(x-18)(x+10)
x=18,x=-10