If the third proportion to 8 and 18 is the same as the fourth proportion to 2, 81, and x2 + 2x + 2, then find the value of x.
Show answer & explanation
Correct answer: A
Explanation
The correct answer is Option 1 i.e. -1.
Calculations:
Third proportion of 8 and 18 = Fourth proportion of 2, 81 and x2 + 2x + 2
According to the question;
⇒ (18 × 18)/8 = [81 × (x2 + 2x + 2)]/2
⇒ 1 = (x2 + 2x + 2)
⇒ x2 + 2x + 2 - 1 = 0
⇒ x2 + 2x + 1 = 0
⇒ x2 + 1x + 1x + 1 = 0
⇒ x(x + 1) + 1(x + 1) = 0
⇒ (x + 1)(x + 1)
⇒ x = -1, -1