If x = \(\sqrt {2}\) - 1,
find 3x5 + 15x4 + 30x3 + 30x2 + 15x + 5.
Answer & explanation
Correct answer: option 3
3x5 + 15x4 + 30x3 + 30x2 + 15x + 5
⇒ 3(x5 + 5x4 + 10x3 + 10x2 + 5x + 1) + 2 ......(i)
We know, (x+1)5 = x5 + 5x4 + 10x3 + 10x2 + 5x + 1
eq. (i) becomes
⇒ 3(x+1)5 + 2
⇒ 3(1 + \(\sqrt {2}\) - 1)5 + 2
= 3 × \( { \left(\sqrt {2}\right) }^{5} \) + 2
= 2 +12\(\sqrt {2}\)