Question

Prove that (√x + 1) · (4√ + 1) · (8√ + 1) · (8√ — 1) = x — 1, (x ∈ R⁺)

Answer 1

Answer:

what is the question I did not understand

Answer 2

The question here is little incorrect and incomplete, here is the complete question.

Prove that $(\sqrt{x} +1).(\sqrt[4]{x} +1).(\sqrt[8]{x}+1).(\sqrt[8]{x}-1)=x-1$, (x∈R⁺)

Proof with Step-by-step explanation:

The given expression is $(\sqrt{x} +1).(\sqrt[4]{x} +1).(\sqrt[8]{x}+1).(\sqrt[8]{x}-1)$-------(1)

Using the formula $(x-a)(x+a)=x^{2} -a^{2}$

equation 1 can be simplified to $(\sqrt{x} +1).(\sqrt[4]{x} +1).(\sqrt[4]{x} -1)$ by multiplying 8th root terms

• This can be further simplified to $(\sqrt{x} +1).(\sqrt{x} -1)$ by multiplying 4th root terms.

• which is equal to x-1 by applying same formula again

therefore, L.H.S. expression obtained is $x-1$,equal to R.H.S.