Question

Find two number with sum 4 and product 2

Answer 1

Let the first number be x.
Sum of the two numbers = 4
∴ Second number = 4 − x
Product of the numbers = 2
⇒ x(4 − x) = 2
⇒ 4x − x2 = 2
⇒ x2 − 4x = −2
Adding 4 to both the sides to make L.H.S a perfect square:
x2 − 4x + 4 = −2 + 4
⇒ x2 − 2 × 2 × x + (2)2 = 2
⇒ (x − 2)2 = 2 {Using a2 + b2 − 2ab = (a − b)2}