Question

The sum of the squire of two number is 233 and one of the number is 3 less than twice the other.find the number

Answer 1

Let two numbers P and Q .
P² + Q² = 233 -----------(1)
P - 2Q = 3 -----------(2)

from equation (1) and (2)

Q² + (2Q + 3)² = 233
Q² + 4Q² + 12Q + 9 - 233 = 0
5Q² + 12Q - 224 = 0

now, discriminant (D) = (12)² + 4×224 × 5
= 144 + 4480
= 4624 = (68)²

$Q=\frac{-12\pm\sqrt{68^2}}{10}\\\\=\frac{-12\pm\:68}{10}\\\\=-8,5.6$

hence, number are -8 , -13 or, 5.6 ,14.2