If x = 23, find the value of x8 - 24x7 + 24x6 - 24x5 + 24x4 - 24x3 + 24x2 - 24x + 1.
Show answer & explanation
Correct answer: A
Explanation
The correct answer is Option 1 i.e. -22.
x8 - 24x7 + 24x6 - 24x5 + 24x4 - 24x3 + 24x2 - 24x + 1
⇒ x8 - (23 + 1)x7 + (23 + 1)x6 - (23 + 1)x5 + (23 + 1)x4 - (23 + 1)x3 + (23 + 1)x2 - (23 + 1)x + 1
Put, 23 = x
⇒ x8 - (x + 1)x7 + (x + 1)x6 - (x + 1)x5 + (x + 1)x4 - (x + 1)x3 + (x + 1)x2 - (x + 1)x + 1
⇒ x8 - x8 - x7 + x7 + x6 - x6 - x5 + x5 + x4 - x4 - x3 + x3 + x2 - x2 - x + 1
⇒ -x + 1
⇒ -23 + 1 = - 22