If 1 + x2 + x4 = 585 and 1 - x + x2 = 65, then find the value of 1 + x + x2.
Show answer & explanation
Correct answer: D
Explanation
The correct answer is option 4 i.e. 9
According to question,
1 + x2 + x4 = 585
1 – x + x2 = 65
1 + x2 + x4 = 585 = (1 - x + x2 )(1 + x + x2 )
Using the a2 - b2 = (a + b)(a - b)
By using the formula,
We get,
⇒ (1 + x + x2 ) = 585/65 = 9
∴ The required value of 1 + x2 + x is 9