The sum of the solutions of the equation + 2 = 0, (x > 0) is equal to
The sum of the solutions of the equation + 2 = 0, (x > 0) is equal to
Let = t
|t − 2| + t(t − 4) + 2 = 0
⇒ |t − 2| + t2 − 4t + 4 − 2 = 0
⇒ |t − 2| + (t − 2)2 − 2 = 0
Let |t − 2| = z (Clearly z ≥ 0)
⇒ z + z2 − 2 = 0
⇒ z = 1 or −2 (rejected)
⇒ |t − 2| = 1 ⇒ t = 1, 3
If = 1 ⇒ x = 1
If = 3 ⇒ x = 9
Sum of solutions = 10