Question

The sum of the square of two number is 233 and one number is 3 less than twice the other no. Find the numbers

Answer 1

Let the numbers be x & y.

x^2 + y^2 = 233

y = 2x - 3

x^2 + (2x - 3)^2 = 233

x^2 + 4x^2 - 12x + 9 = 233

5x^2 - 12x = 224

5x^2 - 12x - 224 = 0 (solve by Quadratic formula)

x = 8, x = -28/5

Let’s take integer value

x = 8

y = 2x - 3

y = 13

Therefore x = 8, y = 13 ——> Answer

Answer 2

Answer:

first number =8

second number=13

Step-by-step explanation:

let a number=x

second number=2x-3

according to statement,

x²+(2x-3)² = 233

x²+(2x)²+(3)²-2(2x)(3)=233

x²+4x²+9-12x=233

5x²-12x+9-233=0

5x²-12x-224=0

5x²-40x+28x-224=0

5x(x-8)+28(x-8)=0

(5x+28)(x-8)=0

5x+28=0            x-8=0

5x=-28               x=8

x=-28/5

therefore number =8

first number =x=8

second number=2x-3

                          =2(8)-3

                          =16-3 =13