Question

A number (x) is 3 less than the thrice of other number (y) and the sum of their squares is 97.
The values of x and y are respectively?

Answer 1

Let the numbers be x and y

According to question,

x = 3y-3....(1)

It is also given that,

x^2 + y^2 = 97

From equation (1),

(3y-3)^2 + y^2 = 97

9y^2 + 9 - 18y +y^2 = 97 [ (a+b)^2 =a^2 + b^2 + 2ab]

10y^2 - 18y - 88 = 0

10y^2 - 40y + 22y - 88 = 0

10y (y - 4) + 22 (y - 4) = 0

(y - 4 )(10y + 22) = 0

=> y - 4 = 0

y = 4

10y + 22 = 0

y = -11/5

Therefore,

y = 4, -11/5