Find the value of \((2^{\frac14}-1)(2^{\frac34}+2^{\frac12}+2^{\frac1

1.	Find the value of \((2^{\frac14}-1)(2^{\frac34}+2^{\frac12}+2^{\frac14}+1)\)(a) 2 (b) 3 (c) 5 (d) 1
Answer» (d) 1 \(\bigg(2^{\frac14}-1\bigg)\bigg(2^{\frac34}+2^{\frac12}+2^{\frac14}+1\bigg)\) Let \(2^{\frac14}\) = a . Then, Given exp. = (a – 1) (a³ + a² + a + 1 ) = (a – 1) (a² (a + 1) + 1(a + 1)) = (a – 1) (a + 1) (a² + 1) = (a² – 1) (a² + 1) = a⁴ – 1 ∴ Required value = \(\big(2^{\frac14}\big)^4\) -1 = 2 - 1 = 1.

Find the value of \((2^{\frac14}-1)(2^{\frac34}+2^{\frac12}+2^{\frac14}+1)\)(a) 2 (b) 3 (c) 5 (d) 1

Answer»

(d) 1

\(\bigg(2^{\frac14}-1\bigg)\bigg(2^{\frac34}+2^{\frac12}+2^{\frac14}+1\bigg)\)

Let \(2^{\frac14}\) = a . Then,

Given exp. = (a – 1) (a³ + a² + a + 1 )

= (a – 1) (a² (a + 1) + 1(a + 1))

= (a – 1) (a + 1) (a² + 1) = (a² – 1) (a² + 1)

= a⁴ – 1

∴ Required value = \(\big(2^{\frac14}\big)^4\) -1 = 2 - 1 = 1.